Studying a simple harmonic motion
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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:
- 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.
- The dots marked on the tape were examined. The motion of the pendulum bob was described.
- Two widely spaced dots on the tape were marked– this gave the zero position of the pendulum bob.
- On the tape every 3rd
Middle
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:
- Measure from the bottom of the heavy stuff to the centre of the ringed mass.
- Do not cause the pendulum to swing through an angle greater than 10 degrees.
- 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.
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