# Pendulem in Simple Harmonic Motion

Laboratory 1 Simple Pendulum Motion

By Ryan Williams Foundation Degree Mechanical Engineering

Introduction

In Mechanics and Physics, simple harmonic motion (SHM) is a periodic motion that is neither driven on damped by external forces. An object in simple harmonic motion experiences a net force which relates to Hooke’s law. Hooke’s law states “Force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction of the displacement”.

Method

For this assignment I am going to try and verify the kinematic simple harmonic motion of a pendulum and compare physical measurements taking with the theory of SHM to verify if the theory is correct. To achieve this I am going to attach a plumb bob to a piece of string suspended from a clamp to allow it to oscillate. Firstly I will measure the length of the pendulum and note the time it takes to complete 30 oscillations, this will be repeated giving me two separate data recordings. From these two readings I will calculate the average time to obtain a more accurate measurement. This will then be repeated six times, each time changing the length of the string.

(Fig 1)

Fig 1 shows a similar method that I am going to use to collect the data required.

Diagram Available [Online] from [http://www.phys.unt.edu/~klittler/demo_room/waves_demos/3a10_10.htm] [accessed 18/02/13]

Results

|Length of string (mm) |√Length (mm)½ |Time for 30 |Average time for 30 |Period (T) | | | |oscillations (s) |oscillations (s) | | |335mm |18.30mm |T1 - 35.28 T2 -|35.55sec |1.19sec | | | |35.81 | | | |500mm |22.36mm |T1 - 47.84 T2 -|47.36sec |1.58sec | | | |46.87 | | | |690mm |26.27mm |T1 - 51.34 T2 -|50.47sec |1.68sec | | | |49.60 | | | |780mm |27.93mm |T1 - 53.22 T2 -|53.24sec |1.77sec | | | |53.25 | | | |870mm |29.50mm |T1 - 55.87 T2 -|55.86sec |1.86sec | | | |55.85 | | | |980mm |31.30mm |T1 - 59.15 T2 -|59.15sec |1.97sec | | | |59.15 | | |

The graph on the previous page represents the data I collected whilst carrying out the pendulum experiment.

The gradient of the line can be worked out using the following equation:

Gradient = Change in y/Change in x

I have chosen to take data points from the mid range of my data to determine the gradient of the best line of best fit.

x = 27.93, y = 53.24

53.24/27.93 = 1.91(2dp)

By the theory of SHM the gradient of the line should be:

This shows the gradient of the line of best fit for the practical data is very close to the gradient worked out using the theory behind SHM....

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