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# Studying a simple harmonic motion

Extracts from this document...

Introduction

Lam Cheuk Ying Regina

F.6C (12)

Date: 15th December, 2009

Title: Studying a simple harmonic motion

Objective: To study the simple harmonic motion (SHM) of a simple pendulum and to investigate how acceleration is related to displacement in a SHM.

Apparatus:

1 ringed mass (0.5kg), 1 string (1.5 m long), 1 ticker- timer, 1 ticker tape, 1 low voltage power supply, 1 retort stand and clamp, 1 heavy stuff (for fixing the stand)

Procedure:

1. The apparatus was set up as shown in the diagram. The 0.5 kg mass was pulled to one side, the ticker-tape timer was started, then the mass was released to swing to the other side. The timer was stopped when the mass reaches the other side.
2. The dots marked on the tape were examined. The motion of the pendulum bob was described.
3. Two widely spaced dots on the tape were marked– this gave the zero position of the pendulum bob.
4. On the tape every 3rd

Middle

/s

Displacement x/m

0

0.37

0.06

0.354

0.12

0.33

0.18

0.296

0.24

0.257

0.3

0.214

0.36

0.163

0.42

0.106

0.48

0.048

0.54

-0.011

0.6

-0.068

0.66

-0.123

0.72

-0.175

0.78

-0.222

0.84

-0.258

0.9

-0.289

0.96

-0.312

1.02

-0.321

• Velocity-time (v-t) graph:
 Time t/s Velocity v/ms-1 0.03 -0.26667 0.09 -0.4 0.15 -0.56667 0.21 -0.65 0.27 -0.71667 0.33 -0.85 0.39 -0.95 0.45 -0.96667 0.51 -0.98333 0.57

Conclusion

• Error estimation:

-The experimental value of T = 2(1.02) = 2.04s

-The theoretical value of T =2π√ (1.5/10) = 2.43 s

% error in T = (2.43-2.03)/2.43 x 100% = 16.5%

• Precautions:
1. Measure from the bottom of the heavy stuff to the centre of the ringed mass.
2. Do not cause the pendulum to swing through an angle greater than 10 degrees.
3. Ensure that the pendulum swings in one plane only, so as to avoid circular movements.

Conclusion:

Simple harmonic motion is a periodic motion which the period of oscillation is independent of the amplitude of the motion. Also, the acceleration of the body is directly proportional to its displacement from a fixed point and is always directed towards that point in a simple harmonic motion. Therefore the equation relating acceleration and displacement can be written as a= - (constant) x.

This student written piece of work is one of many that can be found in our AS and A Level Electrical & Thermal Physics section.

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