sources of error in pendulum experiment

11 Testing the Simple Pendulum Model

Testing pendulum models.

This lab is designed to align with AAOT science outcome #1: Gather, comprehend, and communicate scientific and technical information in order to explore ideas, models, and solutions and generate further questions.

• string or fishing line
• dense object with compact shape (nut or washer, rock, toy car)
• sturdy structure for the object to freely swing from (cabinet handle, horizontal railing, shower curtain)
• protractor ( here is one you can print )
• Ruler, at least 12″ (30 cm) long
• writing utensil
• digital device with spreadsheet program
• digital device with internet access
• Understand the major limitations of the simple pendulum model caused by the assumptions contained in the model.
• Apply the simple pendulum model to experimental data from a variety of real pendula made from objects with different shapes and densities.
• Treat the gravitational acceleration near Earth’s surface ( g ) as a free parameter of the simple pendulum model and extract a value.
• Compare the model prediction for g  to the accepted value.
• Evaluate the overall success of the simple pendulum model in predicting the frequency of real pendula under specific conditions.
• Analyze the time dependence of the pendulum amplitude using a damped oscillator model.

The simple Pendulum Model

The simple pendulum model predicts that the pendulum will behave as a simple harmonic oscillator with the angle of the string away from vertical serving as the displacement. The oscillator frequency will depend only on the length of the pendulum (L) and the gravitational acceleration ( g ) according to the following equation, which we will put to the test in this lab.

The simple pendulum model is derived under the following assumptions:

• The swinging object is a point mass.
• The string (or rod) used to hang the object has no mass.
• There is no air resistance or friction in the system.

2) According to the simple pendulum model, the the oscillation frequency depends on the string length to what power? (Length is raised to what power in the frequency equation at the start of the lab?) Note that no dependence on length means a power of zero. Explain.

3) According to the simple pendulum model, the the oscillation frequency depends on the mass to what power? Explain.

4) According to the simple pendulum model, the the oscillation frequency depends on the oscillation amplitude to what power? (Meaning amplitude is raised to what power in the frequency equation?)  Explain.

Amplitude Experiment

We will test the simple pendulum model by verifying that it correctly predicts how the oscillation frequency on length, mass, and amplitude.

Object:__________

Starting amplitude:__________

Time for 10 Oscillations:__________

6)  Use your time for 10 oscillations to calculate the oscillation period,  frequency, and angular frequency. Show your work.

Amplitude Data

Amplitude analysis.

8) Make a graph of the oscillation frequency vs. amplitude. Be sure to label the graph and the axes, including units.

9) Apply a best fit line and record the fit function and R 2 value here. Does the frequency appear to depend on amplitude? Explain.

Amplitude Conclusions

10) With regard to the dependence of oscillation frequency on amplitude, does the data support the validity of the frequency equation predicted by the simple pendulum model? Explain.

Length Experiment

Length data, length analysis.

12) Make a graph of oscillation frequency vs. length. Make sure that your length data has units of meters. Be sure to label the graph and the axes, including units. Copy and paste your frequency and length data into two new columns of the online spreadsheet.

13) Apply a power law fit to data in the graph of  frequency vs. length. Record the fit equation and R 2 value here:

14) Does the power law model provide a good fit to your data? Explain.

15) According to your fit equation, what is the power on the length variable? Does this agree with the power dependence predicted by the model? [Hint: You plotted frequency vs. length, so “y” in your fit equation is actually “f” and “x” in your equation is actually “L”. Compare the power of x in the fit equation to the power of L in the frequency equation for a simple pendulum]

16) Compare your fit equation to the simple pendulum equation. Rewriting your fit equation, but replacing “y” with “f” and “x” with “L”  will help you remember what the variables in the fit equation mean. If you then write the simple pendulum frequency equation directly below that, you can directly compare each part of each equation. The fit equation indicates that frequency is equal to a coefficient (just a number) multiplied by the length raised to some power. The simple pendulum equation predicts that the frequency is equal to a combination of constants multiplied by the length raised to a power (-1/2). Therefore, if the fit is good, then the combination of constant in the pendulum equation should be equal to the coefficient in the fit equation. Set these equal and solve for g , and calculate a numerical value.

17)  Applying a simple pendulum model to your data has allowed you to extract a value for the free-fall acceleration due to gravity on the surface of Earth without having to actually drop anything in free-fall. Of course your pendulum wasn’t really a perfect simple pendulum, and there is uncertainty in your measurements, both of which lead to error. Compare the value for g that you found with the accepted value for g . Show your work in calculating a % difference.

Length Conclusions

18) With regard to the dependence of oscillation frequency on length, does the data support the validity of the the simple pendulum model? Explain.

MAss Experiment

To provide experimental data on a variety of masses we will combine all of the class data. Your chosen objects will have a variety of masses. If the oscillation frequency is independent of mass and amplitude, as predicted by the simple pendulum model, then we should be able to fit all of the frequency vs. length data with a single equation.

19) Copy and paste the data from your classmates into the frequency and length columns of your own sheet to create one combined dataset. Make a new graph of this data. Be sure to label the graph and the axes, including units.

20) Apply a power fit to the class data. Record the fit equation and R 2 here:

MAss Conclusions

21) With respect to mass, does the class data support the validity of the simple pendulum model? Explain.

Overall Conclusions

22) Overall, do you conclude that the simple pendulum model is valid under the conditions tested by you and your classmates? Explain in terms of the results of each set of analyses you performed.

Further Questions

23) What changes to the experiment would you make to ensure that the experimental conditions more closely matched the assumptions of the simple pendulum model? Explain the reasoning behind your proposed changes.

Modeling a Damped Pendulum

24) The simple pendulum model predicts that the pendulum will behave as a simple harmonic oscillator, which means the pendulum motion can be described by cosine or sine functions and that the amplitude is constant. However, you observed that the amplitude was not constant–the amplitude decreased over time. Explain what caused the decrease.

In some cases the damping force is proportional to the velocity of the oscillator:

25) Label two new with columns with amplitude and time, including units. Watch the video and record the starting amplitude for time zero in your spreadsheet. Next, record the stopwatch time and amplitude on every 5th oscillation until about 1 minute. After one minute the amplitude changes slowly enough that can begin recording the time and amplitude on every 10th oscillation. For each data point you will likely need to use the pause, scrub, and playback speed features of the video player to narrow down when the amplitude fist appeared to drop by a full 0.5 degrees. The playback speed can be adjusted by clicking on the gear in the lower right of the player. 

26) Plot the amplitude vs time, name and label the graph, and apply an exponential fit. Record the equation and R 2 value here:

27) Do the data suggest that the damping forces acting on the pendulum are proportional to the velocity? Explain.

General Physics Remote Lab Manual Copyright © by Lawrence Davis is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

Share This Book

All Lab Experiments

To Study the Random Errors in Determining the Period of a Simple Pendulum

• Physics Practical Files

Find Random Errors Practical file in .pdf format here

Find more Mechanics Practical Files on this Link – https://alllabexperiments.com/phy_pract_files/mech/

Watch this practical on YouTube – https://www.youtube.com/watch?v=zoQXRqPsxYs

Watch this video to understand Errors in Physics Experiments – https://www.youtube.com/watch?v=1fA9DrQiV44

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Related Posts

To study the frequency variation in hartley oscillator.

This Link provides the handwritten practical file of the above mentioned experiment (with readings) in the readable pdf format. ...

To Study the Output and Transfer Characteristics of a Junction Field Effect Transistor (jFET)

To study the i-v characteristics of common drain (cd) configuration of fet.

Required Practical: Investigating SHM ( AQA A Level Physics )

Revision note.

Physics Project Lead

Required Practical: Investigating SHM

Equipment list.

• Stopwatch = ±0.01 s
• Metre Ruler = ±1 mm

SHM in a Mass-Spring System

• This experiment aims to calculate the spring constant of a spring in a mass-spring system
• This is just one example of how this required practical might be carried out
• Independent variable = mass,  m
• Dependent variable = time period,  T
• Spring constant,  k
• Number of oscillations

The setup of apparatus to detect oscillations of a mass-spring system

• Set up the apparatus, with no masses hanging on the holder to begin with (just the 100 g mass attached to it)
• Pull the mass hanger vertically downwards between 2-5 cm as measured from the ruler and let go. The mass hanger will begin to oscillate
• Start the stopwatch when it passes the nail marker
• Stop the stopwatch after 10 complete oscillations and record this time. Divide the time by 10 for the time period (which is the mean)
• Add a 50 g mass to the holder and repeat the above between 8-10 readings. Make sure the mass is pulled down by the same length before letting go
• An example table might look like this:

 Analysing the Results

• Obtain an equation for the spring constant,  k 
• Then plot a suitable graph to obtain a value for k
• Start with the time period of a mass-spring system from the equation:

• T  = time period (s)
• m = mass (kg)
• k = spring constant (N m –1 )
• Squaring both sides of the equation gives:

• Gradient = 4π 2 / k
• The spring constant, k , is therefore equal to:

• Where  T 2 and  m  are directly proportional to each other
• The graph is a straight line with a positive gradient

• Where k is found from the gradient of a force F  extension x  graph

SHM in a Simple Pendulum

• This experiment aims to calculate the acceleration due to gravity of a simple pendulum
• Independent variable = length, L
• Mass of pendulum bob,  m

• Set up the apparatus, with the length of the pendulum at 0.2 m
• Make sure the pendulum hangs vertically downwards at equilibrium and inline directly in front of the needle marker
• Pull the pendulum to the side at a very small angle then let go. The pendulum will begin to oscillate
• Start the stopwatch when the pendulum passes the needle marker in its equilibrium. One complete oscillation occurs when the pendulum passes through the equilibrium, to one maximum and then the other, and back to the equilibrium again (not just from side to side)
• Stop the stopwatch after 10 complete oscillations and record the total time. Divide the time by 10 to obtain the time period (which is the mean)
• Adjust the string to increase the length of the pendulum and the wooden block. Repeat the above for 8-10 readings. The ruler is used to measure the string. Ensure it is measured from the wooden blocks to the centre of mass of the bob.
• Oscillations should be counted as follows:

Analysing the Results

• Obtain an equation for the   acceleration due to gravity, g 
• Then plot a suitable   graph   to obtain a value for g
• The time period of a simple pendulum is given by:

• T = time period (s)
• L = length of the pendulum (m)
• g = acceleration due to gravity (m s –2 )
• Squaring both sides of the equation gives

• gradient m = 4π 2 / g

The acceleration due to gravity is equal to:

• Where  T 2   and  L are   directly proportional   to each other
• The graph is a   straight line   with a   positive gradient

• The accuracy of the experiment can be determined by comparing the obtained value of  g  to the accepted value of acceleration due to gravity,  g = 9.81 m s −2

Evaluating the Experiments

Systematic Errors :

• Reduce parallax error by viewing the marker at eye level

Random Errors :

• Record the time taken for 10 full oscillations, then divide by 10 for one period, to reduce random errors
• For the simple pendulum, the oscillations may not completely go from side to side, and the object may move in a circle. Therefore, keep the amplitudes of oscillation relatively small (only a few cm) and repeat any readings that take a different trajectory
• The equation for the time period of a pendulum bob only works for small angles , so make sure the pendulum is not pulled too far out to the side for the oscillation
• For the mass-spring system, the oscillations may not stay completely vertical. Therefore, keep the amplitudes relatively small (only a few cm) and repeat the readings making sure they are vertical
• When setting an oscillation in motion make sure the mass is pulled to the side by the same angle every time 
• A motion tracker and data logger could provide a more accurate value for the time period and reduce the random errors in starting and stopping the stopwatch (due to reflex times)

Safety Considerations

• Place a soft surface directly below the equipment to reduce the damage caused by a falling pendulum or spring
• Only pull down the mass and spring system a few centimetres for the oscillations, as larger oscillations could cause the masses to fall off and damage the equipment
• The wooden blocks must be tightly clamped together to hold the string for the pendulum in place, otherwise, the pendulum may dislodge during oscillations and fall off

Worked example

A student investigates the relationship between the time period and the mass of a mass-spring system that oscillates with simple harmonic motion. They obtain the following results:

Calculate the value of the spring constant of the spring used in this experiment.

Step 1: Complete the table

Add the extra column T 2 and calculate the values

Step 2: Plot the graph of T 2 against the mass m

Make sure the axes are properly labelled and the line of best fit is drawn with a ruler.

The line of best fit should have an equal number of points above and below it.

Step 3: Calculate the gradient of the graph

The gradient is calculated by:

Step 4: Calculate the spring constant, k

You've read 0 of your 10 free revision notes

Get unlimited access.

to absolutely everything:

• Downloadable PDFs
• Unlimited Revision Notes
• Topic Questions
• Past Papers
• Model Answers
• Videos (Maths and Science)

Join the 100,000 + Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.

Stack Exchange Network

Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Q&A for work

Connect and share knowledge within a single location that is structured and easy to search.

Error propagation with a pendulum

The following is a 2018 F=ma exam question. I know that this isn't a homework site, but I think that my question is conceptually relevant. Here's the problem:

A group of students wish to measure the acceleration of gravity with a simple pendulum. They take one length measurement of the pendulum to be $l = 1.00 \pm 0.05\ \rm m$ . They then measure the period of a single swing to be $T = 2.00 \pm 0.10\ \rm s$ . Assume that all uncertainties are Gaussian. The computed acceleration of gravity from this experiment illustrating the range of possible values should be recorded as A) $9.87 \pm 0.10\ \rm{m/s^2}$ B) $9.87 \pm 0.15\ \rm{m/s^2}$ C) $9.9 \pm 0.25\ \rm{m/s^2}$ D) $9.9 \pm 1.1\ \rm{m/s^2}$ E) $9.9 \pm 1.5\ \rm{m/s^2}$

I know that the pendulum period formula is $T = 2\pi\sqrt{l/g}$ , and therefore, that $g = \frac{4\pi^2l}{T^2}$

I don't know much about this error stuff, so I went about it in a fairly straightforward way and I still can't seem to find the flaw:

Obviously the biggest value for $g$ will be when $l$ is biggest and $T$ is smallest. The biggest $l$ is $1.00 + 0.05 = 1.05$ . The smallest $T$ is $2.00 - 0.10 = 1.90$ . $4\pi^2\times 1.05/(1.90)^2 = 11.48$ .

The smallest value for $g$ is when $l$ is smallest and $T$ is biggest. Going through the same process, you get $g = 8.50$ . The difference between those two values is $2.97$ which is about $3$ . Therefore, the error has to be something $\pm 1.5$ , which would make the answer E. It is not E, but D.

The solution on the F=ma website said complicated things about adding squares of error and things I haven't learned.

So my question is what is wrong with my logic here?

• homework-and-exercises
• harmonic-oscillator
• error-analysis

• $\begingroup$ Acvording to what you have provided, the answer is indeed E and not D $\endgroup$ –  Paul Childs Commented Jan 11, 2019 at 0:43

3 Answers 3

The problem with your method is that it implicitly assumes the errors are (anti)correlated. Well, what does that mean?

It means you assume that when the length fluctuates high (low), then the period measurement must fluctuate low (high). Since a larger (smaller) length and a shorter (longer) time both increase (decrease) the value of $g$ , the fluctuations in $g$ are overestimated.

The question then is, how do you add uncorrelated errors? Answer: in quadrature. The next question is, why in quadrature? You could write books on that, but in short, it's the Pythagorean theorem:

$$ a^2 + b^2 = c^2 $$

which is exactly how you add uncorrelated lengths.

A somewhat loose explanation is, suppose:

$$ C = AB $$

and you measure:

$$ A \pm a $$

$$ B \pm b $$

What is the uncertainty in $C$ ?

Well, gaussian errors are distributed as:

$$ P_a(a) \propto e^{-a^2} $$

$$ P_b(b) \propto e^{-b^2}$$

$$ P_c(a, b) \propto P_a(a)P_b(b) $$ $$ P_c(a, b) = e^{-a^2}e^{-b^2} = e^{-(a^2+b^2)}\equiv e^{-c^2} =P_c(c) $$

where the fluctuations in $C$ given by those in $A$ and $B$ added in quadrature:

$$ c = \sqrt{a^2 + b^2}$$

• $\begingroup$ But when you want to describe the range of possibility, don't you want to consider the worst case? $\endgroup$ –  QFTUNIverse Commented Jan 11, 2019 at 15:22
• $\begingroup$ @QFTUNIverse When you quote a 1 sigma error bar made from 1 sigma errors, you want exactly that: a 1 sigma variance--not the worst case. Now I have worked projects were we have included 99-percentile cases (1% chance), but then you're doing quantiles, and it's a bit more complicated. BTW: on 2nd thought, my "loose" explanation is too loose (unless $A=B$). $\endgroup$ –  JEB Commented Jan 11, 2019 at 17:12

When you give a measurement result with an extended standard uncertainty, you set a probability that the "true" value is in your range. For example, the probability that the true value of $l$ is between 0.95 and 1.05 is 95%. Or, the probability that the value is not in this range is 5%. Same idea for $T$ .

As a result, your calculation is too pessimistic. You put yourself in the situation for which the errors would be maximum on both $l$ and on $T$ which is "unlikely". Without accurate calculation, you can understand that the probability that the true value of $g$ is outside your range is less than 5%. This is the reason why, most often, it is the squares of uncertainties that are added.

An error equation is obtained from the differential of the equation. Take the differential operator of both sides and you get:

dg = 4 pi^2 (dI/T^2 - 2IdT/T^3)

dg/g = dI/I - 2dT/T

As we are after the magnitude of errors, the negative sign gets switched for a plus. There's a bit more to it but with uncorrelated guassian errors it works out smoothly. The equation is then one of relative errors.

• $\begingroup$ As I said in my question, I know basically nothing about error propagation. My question was less about the proper solution and more about what is wrong with the method I was using. $\endgroup$ –  QFTUNIverse Commented Jan 11, 2019 at 1:08
• $\begingroup$ Methodology wise you were looking at maximum and minimum errors. The key is that the errors are guassian so don't have a min/max but a variance. $\endgroup$ –  Paul Childs Commented Jan 11, 2019 at 2:05

Your Answer

Sign up or log in, post as a guest.

Required, but never shown

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy .

Not the answer you're looking for? Browse other questions tagged homework-and-exercises harmonic-oscillator error-analysis or ask your own question .

• Featured on Meta
• Bringing clarity to status tag usage on meta sites
• We've made changes to our Terms of Service & Privacy Policy - July 2024
• Announcing a change to the data-dump process

Hot Network Questions

• "Knocking it out of the park" sports metaphor American English vs British English?
• Fitting 10 pieces of pizza in a box
• I can't select a certain record with like %value%
• Can the speed of light inhibit the synchronisation of a power grid?
• Adding equations of motion
• Why HTTPS requests are working with dynamic IP address, and not with static IP address
• The meaning of “manage” in this context
• Can objective morality be derived as a corollary from the assumption of God's existence?
• What language did Descartes use when he lived in the Netherlands?
• How soon to fire rude and chaotic PhD student?
• How old were Phineas and Ferb? What year was it?
• Everyone hates this Key Account Manager, but company won’t act
• Population impacts on temperature
• Why are swimming goggles typically made from a different material than diving masks?
• Should it be "until" or "before" in "Go home until it's too late"?
• Consistency strength of HoTT
• The McDonald's Option
• Is sudoku only one puzzle?
• Is a monoid endomorphism determined by its right inverse?
• How to remove files which confirm to a certain number pattern
• 1969s-1970s novel, mankind needs to emigrate to escape Sun going nova, women are higher status than men, men have artificial snake familiars
• How many people could we get off of the planet in a month?
• Why is global state hard to test? Doesn't setting the global state at the beginning of each test solve the problem?
• Why do combinatorists care about Kazhdan–Lusztig polynomials?

Simple Pendulum Experiment Class 11 | Labkafe

Using a simple pendulum, plot its L-T2 graph and use it to find the effective length of second’s pendulum.

• A Clamp With Stand
• Bob with Hook
• Stop Clock/Stop Watch
• Vernier Callipers
• Cotton Thread
• Half Meter Scale

A simple pendulum consists of a heavy metallic (brass) sphere with a hook (bob) suspended from a rigid stand, with clamp by a weightless inextensible and perfectly flexible thread through a slit cork, capable of oscillating in a single plane, without any friction, with a small amplitude (less than 150) as shown in figure 6.1 (a). There is no ideal simple pendulum. In practice, we make a simple pendulum by tying a metallic spherical bob to a fine cotton stitching thread.

               The spherical bob may be regarded by as a point mass at its centre G. The distance between the point of suspension S and the centre G of the spherical bob is to be regarded as the effective  length of the pendulum as shown in figure 6.1 (b). The effective length of a simple pendulum,  L = l + h + r.  Where  l  is the length of the thread,  h  is length of hook,  r  is radius of bob.

The simple pendulum produces Simple Harmonic Motion (SHM) as the acceleration of the pendulum bob is directly proportional to its displacement from the mean position and is always directed towards it. The time period (T) of a simple pendulum for oscillations of small amplitude, is given by the relation,

T = 2 π √ (L/g)

Where, g = value of acceleration due to gravity and L is the effective length of the pendulum.

 T2 = (4π2/g) X L             or           T2 = KL (K= constant)

               and,  g = 4π2(L/T2)

If T is plotted along the Y-axis and L along the X-axis, we should get a parabola. If T2 is plotted along the Y- axis and L along the X-axis, we should get a straight line passing through the origin.

• Find the vernier constant and zero error of the vernier callipers same as experiment 1.
• Measure the radius (r) of the bob using a vernier callipers same as experiment 1.
• Measure the length of hook (h) and note it on the table 6.1.
• Since h and r is already known, adjust the length of the thread  l  to make  L = l + h + r  an integer (say L = 80cm) and mark it as M1 with ink. Making L an integer will make the drawing easier. (You can measure the distance between the point of suspension (ink mark) and the point of contact between the hook and the bob directly. Hence you get  l + h  directly).
• Similarly mark M2, M3, M4 , M5, and  M6 on the thread as distance (L) of 90 cm, 100 cm, 110cm, 120cm and 130 cm respectively.
• Pass the thread through the two half-pieces of a split cork coming out just from the ink mark (M1).
• Tight the split cork between the clamp such that the line of separation of the two pieces of the split cork is at right angles to the line along which the pendulum oscillates.
• Fix the clamp in the stand and place it on the table such that the bob is hanging at-least 2 cm above the base of the stand.
• Mark a point A  on the table (use a chalk) just below the position of bob at rest and draw a straight line BC of 10 cm having a point A at its centre. Over this line bob will oscillate.
• Find the least count and the zero error of the stop clock/watch. Bring its hands at zero position
• Move the bob by hand to over position B on the right of A and leave. See that the bob returns over line BC. Make sure that bob is not spinning.
• Now counting oscillations, from the instant bob passes through its mean position L, where its velocity is maximum. So starting from L it traverses LL2, L2L, LL1, L1L hence, one oscillation is completed. We have to find time for 20 such oscillations.
• Now start the stop watch at the instant the bob passes through the mean position A. Go on counting the number of oscillations it completes. As soon as it completes 20 oscillations, stop the watch. Note the time t for 20 oscillations in the table 6.1.
• Repeat the measurement at least 3 times for the same length.
• Now increase the length of the thread by 10 cm or 15 cm (M2) and measure the time t for this length as explained from step 6 to 14.
• Repeat step 15 for at least 4 more different lengths.

Observations:

Vernier constant

Vernier constant of the vernier callipers, V.C. = ______________ cm

Zero error, ±e = _____________cm

Diameter of the bob and length of hook

Observe diameter of the bob:= (i) ______cm, (ii)________cm, (iii)___________cm

Mean diameter of bob, d0 = _________cm

Mean corrected diameter of bob, d = d0 ±e = __________cm

Radius of the bob, r = d/2= ____________ cm

Length of the hook, h= __________cm

Standard value acceleration due to gravity, g1 : 980 cm s-2

Least count of stop clock = ____________s

Zero error of stop clock = ___________s

Table 6.1 Determination of time-periods for different lengths of the pendulum.

Mean  = L/T2 = _______________________

Calculation:

We know ,  T = 2 π √ (L/g)

 Experimental value, g1 = 4π2(L/T2) = ______________________

So, %error = (g-g1)/g *100 = ______________________

L vs T graph

Plot the graph between L and T from the observations recorded in the table 6.1. Take L along X-axis and T along Y-axis. The L-T curve is a parabola. As shown in the figure 6.2. The origin need not be (0,0) point.

L vs T2 Graph

Plot the graph between L and T2 from the observations recorded in the table 6.1. Take L along X-axis and T2 along Y-axis. The L-T curve is a straight line passing through the (0, 0) point. So the origin of the graph should be chosen (0, 0). As shown in the figure 6.3.

Determination of length of a seconds pendulum from graph:

A second pendulum has time-period 2 s. To find the corresponding length of the pendulum from the L-T graph, draw a line parallel to the L-axis from the point Q1 (0, 2). The line interval the curve L-T at P1. So, the coordinates of P1 is (102, 2).

 Length of the seconds pendulum is _____________(102) cm.

To find the length from the L-T2 curve, we, similarly, draw a line parallel to L-axis is form a point Q2 (0, 4). The line intersects the curve at P2. P2 has coordinates (100, 4).

 Length of the seconds pendulum is _______________(100) cm.

Precautions :

• The thread should be very light and strong.
• The point of suspension should be reasonably rigid.
• The pendulum should oscillate in the vertical plane without any spin motion.
• The floor of the laboratory should not have vibration, which may cause a deviation from the regular oscillation of the pendulum.
• The amplitude of vibration should be small (less than 15) .
• The length of the pendulum should be as large as possible in the given situation.’
• Determination of time for 20 or more oscillations should be carefully taken and repeated for at least three times.
• There must not be strong wind blowing during the experiment.
• http://www.ncert.nic.in/
• https://www.learncbse.in/

you may download Simple Pendulum Experiment Class 11 practical manual .pdf Download Now

About Labkafe: Lab Equipment Manufacturer & Exporter

We are a School laboratory furniture and Lab equipment manufacturer and supplier. In laboratory furniture for school, we first design the entire laboratory room keeping in mind the requirements as per affiliation CBSE Bye-Laws. Also, we take care of the complete designing and installation of laboratory furniture.

In the lab equipment section, we have a wide range of glassware, chemicals, equipment and other lab accessories. Most of them are available for order online on our website but some of them can be procured on demand.

If you have need:-

• laboratory equipment or lab furniture requirements for school
• composite lab equipment list for school
• Physics lab equipment list for school
• Chemistry lab equipment list for
• Biology lab equipment list for school
• Pharmacy lab equipment

do drop a message through chat or mail us at  [email protected]  or call contact us +919147163562 and we’ll get in touch with you.

Get in Touch

Get A Free Lab Consultation

Leave a reply cancel reply.

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Suggested Reads

Special Features

Vendor voice.

Microsoft patches scary wormable hijack-my-box-via-IPv6 security bug and others

Plus more pain for intel which fixed 43 bugs, sap and adobe also in on the action.

Patch Tuesday Microsoft has disclosed 90 flaws in its products – six of which have already been exploited – and four others that are listed as publicly known.

There's another dozen in the list from third-party vendors that are now included in Microsoft's monthly update. Happy August Patch Tuesday, folks. Of the 102 total bugs listed this month, nine are rated critical, though so far none of those ones seem to have been found and abused by the bad guys.

Holy grail security flaw

First, let's get right to CVE-2024-38063 , this is a zero-click, wormable remote code execution hole in Windows that requires no authentication and is exploited using IPv6 packets. It's pretty bad; it's a 9.8-out-of-10 on the CVSS severity scale.

If someone can craft the correct IPv6 packets to send to your vulnerable Windows machine via the local network or the internet, they can take over that box, install malware or ransomware, steal data, and more. This happens at the TCP/IP stack level in the operating system. There are no exploits for it yet that we know of. Redmond credited someone called Wei at Cyber KunLun's Kunlun Lab for discovering and reporting it.

"An unauthenticated attacker could repeatedly send IPv6 packets, that include specially crafted packets, to a Windows machine which could enable remote code execution," the Azure giant said.

That needs to be patched ASAP before someone figures out how to abuse it in the wild and uses it to hijack computers around the world. All we know so far is that it involves an integer underflow, which may be tricky to exploit in practice though Microsoft says it thinks exploitation is likely at some point.

There's also another 9.8 bug, CVE-2024-38140 , a use-after-free in the Windows Reliable [sic] Multicast Transport Driver that can be exploited again to achieve remote code execution on a vulnerable computer without authentication needed.

"An unauthenticated attacker could exploit the vulnerability by sending specially crafted packets to a Windows Pragmatic General Multicast (PGM) open socket on the server, without any interaction from the user," says Microsoft, adding:

This vulnerability is only exploitable only if there is a program listening on a Pragmatic General Multicast (PGM) port. If PGM is installed or enabled but no programs are actively listening as a receiver, then this vulnerability is not exploitable.

PGM does not authenticate requests so it is recommended to protect access to any open ports at the network level (e.g. with a firewall). It is not recommended to expose a PGM receiver to the public internet.

Another of the critical bugs being patched today: CVE-2024-38160 , remote code execution hole in Windows Network Virtualization. This bug is a heap buffer overflow. This appears to be a useful way to attack other customers in a public cloud setting using Redmond's technologies. It allows someone to move from their virtual machine's confines to the host hypervisor server, and then get into other people's guests.

"This vulnerability could lead to the attacker gaining the ability to interact with other tenant’s [sic] applications and content," says Microsoft.

"An attacker could exploit the vulnerability by taking advantage of the unchecked return value in the wnv.sys component of Windows Server 2016. By manipulating the content of the Memory Descriptor List (MDL), the attacker could cause unauthorized memory writes or even free a valid block currently in use, leading to a critical guest-to-host escape."

Network Virtualization has another critical flaw, CVE-2024-38159 , that works pretty much the same way as above.

And there's also CVE-2024-38166 in Microsoft Dynamics 365 (a cross-site scripting hole), CVE-2024-38206 in Microsoft Copilot Studio that can cause the AI suite to "leak sensitive information over a network," and CVE-2024-38109 in the Azure Health Bot that could be used to elevate privileges.

Regarding the bot, Microsoft says: "This vulnerability has already been fully mitigated by Microsoft. There is no action for users of this service to take. This purpose of this CVE is to provide further transparency."

As said, none of these critical holes have been attacked in the wild that we know of, yet.

Phew, so what's under attack already?

Now for the six bugs under active exploitation:

CVE-2024-38189 – a Microsoft Project Remote Code Execution Vulnerability with an 8.8 CVSS rating. The bad news is it's an RCE and was exploited before it issued a fix.

The good news is exploitation requires a couple of security features to be disabled before an attacker can remotely execute code on a victim's machine. Assuming a criminal can find a way on someone's system to run macros downloaded from the internet (which ain't hard , see the Mark Of The Web hole below, for instance) and also has the block macros from running in Office files from the internet policy disabled, and convinces a victim to open a malicious file, it's game over. Obviously, someone has managed to navigate those hoops, although we have no details on the exploitation, or how widespread it is.

CVE-2024-38178 – a Scripting Engine Memory Corruption Vulnerability that earned a 7.5 CVSS. Microsoft says the attack complexity is high on this one, and it requires the victim to use Edge in Internet Explorer Mode. Apparently some orgs and their websites still really like this dead web browser that Microsoft stopped supporting two years ago.

Once Edge is in Internet Explorer mode, if an attacker can convince the victim to click on a specially crafted URL they can execute remote code on the victim's device.

Redmond credits south Korea's National Cyber Security Center and AhnLab with finding and reporting this vulnerability.

CVE-2024-38193 – a 7.8 rated Windows Ancillary Function Driver for WinSock Elevation of Privilege Vulnerability. This one could allow an attacker to gain system privileges.

As Zero Day Initiative's Dustin Childs noted : "These types of bugs are typically paired with a code execution bug to take over a target. Microsoft doesn't provide any indication of how broadly this is being exploited, but considering the source, if it's not in ransomware already, it likely will be soon."

Gen Digital bug hunters Luigino Camastra and Milánek disclosed the flaw to Redmond.

CVE-2024-38106 – a Windows Kernel Elevation of Privilege Vulnerability with a 7.0 CVSS rating.

Exploiting this bug requires an attacker to win a race condition, but Redmond doesn't provide any details about what that race involves. But once that happens the miscreant can gain system privileges. It's been exploited, so patch soon.

CVE-2024-38107 – a 7.8-rated Windows Power Dependency Coordinator Elevation of Privilege Vulnerability. It could also result in system privileges and has been exploited in the wild.

CVE-2024-38213 – a Windows Mark of the Web Security Feature Bypass Vulnerability that earned a 6.5 CVSS rating.

ZDI researcher Peter Girnus found and reported this vulnerability, which allows an attacker to bypass the SmartScreen security feature. It does, however, require the mark to open a malicious file.

• AMD won't patch Sinkclose security bug on older Zen CPUs
• Using 1Password on Mac? Patch up if you don't want your Vaults raided
• Google splats device-hijacking exploited-in-the-wild Android kernel bug among others
• Six ransomware gangs behind over 50% of 2024 attacks

Microsoft listed four vulnerabilities as publicly disclosed, albeit not yet exploited, so maybe put these high on your to-patch list:

• CVE-2024-38200 – a Microsoft Office Spoofing Vulnerability with a 6.5 CVSS rating.
• CVE-2024-38199 – a Windows Line Printer Daemon (LPD) Service RCE Vulnerability with a 9.8 CVSS rating.
• CVE-2024-21302 – a Windows Secure Kernel Mode Elevation of Privilege Vulnerability with a 6.7 CVSS rating.
• CVE-2024-38202 – a Windows Update Stack Elevation of Privilege Vulnerability with a 7.3 CVSS rating.

Adobe addresses 71 CVEs

Adobe this month fixed 71 CVEs in 11 updates across its Illustrator , Dimension , Photoshop , InDesign , Acrobat and Reader , Bridge , Substance 3D Stager , Commerce , InCopy , 3D Sampler , and Substance 3D Designer products. Adobe states it's not aware of any exploits for any of the now-fixed flaws.

Commerce is the buggiest of the bunch, with seven critical-rated vulnerabilities. InDesign addressed 13 CVEs and Acrobat and Reader fixed 12 – both of which included RCEs.

SAP slaps out 25 security patches

SAP this month released 25 new or updated security patches, including two HotNews notes and four high-priority notes. Thomas Fritsch, SAP Security Researcher at Onapsis, says this count is above average for the software maker.

Of the new HotNews notes, #3479478 ( CVE-2024-41730 ) earned a 9.8 CVSS rating and addresses a denial of service vulnerability in the SAP BusinessObjects Business Intelligence Platform.

"If Single Sign On Enterprise authentication is enabled, an unauthorized user can get a logon token using a REST endpoint," Fritsch warned . "The attacker can fully compromise the system resulting in high impact on confidentiality, integrity and availability."

43 more pain points for Intel

Intel joined the patch party this month with a whopping 43 security advisories that plug multiple holes in software and hardware. Nine are rated high-severity flaws, so let’s start there:

Intel Ethernet Controllers and Adapters fixes CVEs that may allow escalation of privilege or denial of service.

Bugs in some Intel NUC BIOS Firmware may allow escalation of privilege, denial of service and information disclosure.

Vulnerabilities in Intel Core Ultra Processor and Intel Processor stream cache mechanisms may allow escalation of privilege.

Flaws in Intel Trust Domain Extensions (Intel TDX) module software may allow denial of service.

A security vulnerability in SMI Transfer monitor (STM) may allow escalation of privilege.

Flaws in some Intel Agilex FPGA Firmware and some Intel Server Board S2600ST Family Firmware may allow escalation of privilege.

Finally, some Intel UEFI Integrator Tools on Aptio V for Intel NUC are vulnerable to an escalation of privilege bug. ®

Editor's note: This article was updated to draw attention to the wormable IPv6 flaw in Microsoft Windows and other critical flaws.

• Patch Tuesday

Narrower topics

• Active Directory
• Advanced persistent threat
• Application Delivery Controller
• Authentication
• Common Vulnerability Scoring System
• Creative Cloud
• Cybersecurity
• Cybersecurity and Infrastructure Security Agency
• Cybersecurity Information Sharing Act
• Data Breach
• Data Protection
• Digital certificate
• Exchange Server
• Identity Theft
• Incident response
• Intel Optane
• Internet Explorer
• Kenna Security
• Microsoft 365
• Microsoft Build
• Microsoft Edge
• Microsoft Ignite
• Microsoft Office
• Microsoft Surface
• Microsoft Teams
• Palo Alto Networks
• Pat Gelsinger
• Quantum key distribution
• Remote Access Trojan
• RSA Conference
• Surveillance
• Trusted Platform Module
• Visual Studio
• Visual Studio Code
• Vulnerability
• Windows Server
• Windows Server 2003
• Windows Server 2008
• Windows Server 2012
• Windows Server 2013
• Windows Server 2016
• Windows Subsystem for Linux

Broader topics

• Patch Management

Send us news

Other stories you might like

Microsoft's patch tuesday borks dual-boot linux-windows pcs, microsoft pushing, pushing, pushing edge in defender slammed as a 'dark pattern', intel's processor failures: a cautionary tale of business vs engineering, when building the future, the past is no longer a guide.

UK competition regulator's cloud probe remedies have global implications

Intel's legal troubles mount after plunging stock sparks yet another court battle, intel's microcode fix to save raptor lake chips may only work with default power settings, post-crowdstrike, microsoft to discourage use of kernel drivers by security tools, microsoft punches back at delta air lines and its legal threats, if you give copilot the reins, don't be surprised when it spills your secrets, multiple flaws in microsoft macos apps unpatched despite potential risks, it's all drying up: microsoft to erase 3d paint from digital store.

• Advertise with us

Our Websites

• The Next Platform
• Blocks and Files

Your Privacy

• Cookies Policy
• Privacy Policy
• Ts & Cs

Copyright. All rights reserved © 1998–2024

• Intro Physics Homework Help
• Advanced Physics Homework Help
• Precalculus Homework Help
• Calculus Homework Help
• Bio/Chem Homework Help
• Engineering Homework Help

Follow along with the video below to see how to install our site as a web app on your home screen.

Note: This feature may not be available in some browsers.

• Homework Help
• Introductory Physics Homework Help

Uncertainty with a simple pendulum

• Thread starter aborder
• Start date Sep 25, 2011
• Tags Pendulum Simple pendulum Uncertainty
• Sep 25, 2011
• Freeze-frame: Researchers develop world's fastest microscope that can see electrons in motion
• A maximally entangled quantum state with a fixed spectrum does not exist in the presence of noise, mathematician claims
• New heaviest exotic antimatter nucleus discovered

A PF Mountain

aborder said: A simple pendulum is used to measure the acceleration of gravity using T=2pi(sqrt(L/g)) . The period T was measured to be 1.24 ± 0.02 s and the length L to be 0.381 ± 0.002 m. What is the resulting value for g with its absolute and relative uncertainty? So the first thing I did was to isolate g. But to actually calculate the uncertainty, I am completely lost here. I am using the book "Experimentation" by D.C. Baird and nothing is making sense here. Most likely it talks about it in the book, but I am having a hard time understanding this. If someone could explain how to calculate uncertainty for this, it would probably help. Thanks.

• Sep 26, 2011

aborder said: That makes sense to divide by the highest and multiply by the lowest to get the low end and vice versa. Using the method you described, I got 9.79 +/- 0.184. The answer in the book gives 9.77 +/-0.04 with a relative uncertainty of 0.4%. The relative uncertainty is given by this: Relative uncertainty = Absolute Uncertainty / Measured Value

PeterO said: Firstly, my error. I should have said you add the percentage errors not multiply them - haven't used percentage errors for a while. Period T 1.24 +-0.02 means an error of 2 in 124 = 1.6% Length L = 0.381 +- 0.004 means an error of 4 in 381 = 1.05% So total error = 1.6 + 1.6 + 1.05 = 4.25% so 9.78 +- 4% or 9.78 +- .04 I [almost]agree with your numbers, and would express it as 9.78 +- 0.04 or 9.78 +- 4% I wonder if you mis-read the book and they actually had +- 4% not +- 0.4% Note: I can only get your 9.79 if I assume pi = 22/7. I can only get their 9.77 if I assume pi = 3.14. Given that my calculator gives pi to about 10 decimal places, I used them all to get 9.78.

Related to Uncertainty with a simple pendulum

1. what is uncertainty in relation to a simple pendulum.

Uncertainty, also known as error or deviation, refers to the degree of inaccuracy or variability in a measurement or calculation. In the case of a simple pendulum, uncertainty can arise from factors such as human error, environmental conditions, or limitations of the measuring instruments.

2. How is uncertainty calculated in a simple pendulum experiment?

Uncertainty is typically calculated using the standard deviation formula, which takes into account the differences between individual measurements and the average value. This value can then be used to determine the range of possible values within which the true measurement is likely to fall.

3. What is the significance of uncertainty in a simple pendulum experiment?

Uncertainty is an important factor to consider in any scientific experiment, as it can affect the accuracy and reliability of the results. In the case of a simple pendulum, uncertainty can impact the determination of important variables such as the period or length of the pendulum, which in turn can affect the conclusions drawn from the experiment.

4. How can uncertainty be reduced in a simple pendulum experiment?

There are a few ways to reduce uncertainty in a simple pendulum experiment. One method is to take multiple measurements and calculate an average value, which can help to minimize the impact of any individual errors. Additionally, using more precise measuring instruments and controlling environmental factors can also help to reduce uncertainty.

5. What are some common sources of uncertainty in a simple pendulum experiment?

Some common sources of uncertainty in a simple pendulum experiment include human error in recording measurements or starting and stopping the pendulum, variations in the length or weight of the pendulum, and external factors such as air resistance or temperature. These sources of uncertainty should be carefully considered and controlled in order to obtain more accurate results.

Similar threads

• Dec 1, 2021
• Sep 23, 2015
• Jan 1, 2024
• Nov 7, 2023
• Sep 26, 2020
• Dec 12, 2023
• Sep 23, 2023
• Oct 16, 2023
• Oct 28, 2020
• Oct 24, 2022

Hot Threads

• Small oscillations of a simple pendulum placed on a moving block
• How to Calculate Water Leakage in an Inverted Bottle Experiment?
• Vertical displacement with time of a projectile
• Acceleration in uniform circular motion is uniform or non-uniform?
• Help again in interpreting a pulley with a spring and a block

Recent Insights

• Insights   PBS Video Comment: “What If Physics IS NOT Describing Reality”
• Insights   Aspects Behind the Concept of Dimension in Various Fields
• Insights   Views On Complex Numbers
• Insights   Addition of Velocities (Velocity Composition) in Special Relativity
• Insights   Schrödinger’s Cat and the Qbit
• Insights   The Slinky Drop Experiment Analysed