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# Pendulum work out the value of acceleration due to gravity (g), by using the principle of kinematics of simple harmonic motion of a simple pendulum.

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Introduction

Name: Ankit Chowdhary

No:274 T

Physics Laboratory Report

• Research Question-

To work out the value of acceleration due to gravity (g), by using the principle of kinematics of simple harmonic motion of a simple pendulum.

• Introduction-

The theory involved here is the motion of the simple pendulum under the influence of acceleration due to gravity. The research question here says that the value of acceleration due to gravity is an unknown variable and this has to be calculated out using the equation that relates the time period of one oscillation of a simple pendulum (made up of a string with negligible mass and a mass bob having a certain predetermined and set mass) and the length of its string and acceleration due to gravity by the following relation: This investigation is particularly useful in the real world as it gives us a value of the variable acceleration due to gravity, which influences all spheres of mechanics. The equation is also useful as I help determine the value of time that the pendulum will take in one oscillation, thus having applications in instruments such as clocks etc.

• Hypothesis-

According to my prior understanding and visualizations the investigations undertaken will yield the required results effectively and with efficiency. The length of the pendulum would include the length of the string as well as the diameter of the mass bob and the length of the hook as well. When the pendulum suspended from a stand is set into oscillation the time periods ‘T’ of the oscillations of different lengths ‘l’ will help us in determining the value of “g”.

...read more.

Middle

Time(10 Oscillations)

Time (1 Oscillation)

1.

11.5s

1.15s

2.

11.5s

1.15s

3.

11.5s

1.15s

1. For pendulum of length 42.39cm:
 Time(10 Oscillations) Time (1 Oscillation) 1. 13.3s 1.33s 2. 13.2s 1.32s 3. 13.2s 1.32s
1. For pendulum of length 52.39cm:
 Time(10 Oscillations) Time (1 Oscillation) 1. 14.7s 1.47s 2. 14.7s 1.47s 3. 14.7s 1.47s
1. For pendulum of length 62.39cm:
 Time(10 Oscillations) Time (1 Oscillation) 1. 16.2s 1.62s 2. 16.2s 1.62s 3. 16.2s 1.62s
1. For pendulum of length 72.39cm:
 Time(10 Oscillations) Time (1 Oscillation) 1. 17.4s 1.74s 2. 17.3s 1.73s 3. 17.2s 1.72s
1. For pendulum of length 82.39cm:
 Time(10 Oscillations) Time (1 Oscillation) 1. 18.5s 1.85s 2. 18.4s 1.84s 3. 18.3s 1.83s
1. For pendulum of length 92.39cm:
 Time(10 Oscillations) Time (1 Oscillation) 1. 19.2s 1.92s 2. 19.3s 1.93s 3. 19.2s 1.92s
• Processing of Raw Data -

To plot an appropriate graph the plot variables that have been selected by me are length and time period of the pendulums. According to the equation: L = t2. Readings of length of the pendulums are already stated. These are plot variables on their own and do not need to be accounted for errors as they zero error have already been taken care of. The plot variable that needs to be processed is thus t2.

As the value of only t has been taken, the square of time period of 1 oscillation will be the value of t2. On calculating the value of t2 was found out to be:

 Time (t) Time2 (t2) 1. 0.
...read more.

Conclusion will be = 0.41 units. The value of ‘g’ will thus be . (We have to multiply the equation by 100 as he values of ‘g’ calculated by the graph has to be in standard SI Units, and as we have taken all values of length as in cm, we must multiply by hundred to convert these values to meters). From this we get the value of g to be equal to 9.65 ms-2 which taken from the literature value of it is 0.16 ms-2 away from the mark. Hence the percentage error is 1.63%.
• Evaluation-

The methods used were according to me accurate and the results were also seen to have come out to be accurate. The conditions under which this experiment was performed were nothing out of the ordinary, as it was done in a standard room. The limitations and the weaknesses are confined to a few random errors and a systematic error which was found in the vernier calipers. To reduce the errors the following precautions were taken:

1. Errors in the instrument must be considered beforehand.
2. Readings and calculations must be checked.
3. The pendulum must not swing in a circular motion but in a straight motion.
4. Lengths of the string should be taken after taking in account the stretching of the string.
5. Finally, the values must be read correct to the right decimal place and significant figure.

Citations-

1. {http://www.saburchill.com/physics/practicals/006.html}. This was referred to for the literature value of ‘g’.
2. http://www.iop.org/activity/education/Teaching_Resources/Teaching%20Advanced%20Physics/Vibrations%20and%20Waves/Images%20300/img_tb_4434.gif. This source was referred to for the diagram.
3. http://cache.eb.com/eb/image?id=2471&rendTypeId=4. this was referred to for the diagram showing the oscillation of a pendulum.

...read more.

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