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Simple Harmonic Motion

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Introduction

Title: Simple Harmonic Motion

Objective:

Show that the motion of a simple pendulum is simple harmonic, sinusoidal and

independent of amplitude.

Introduction:
   

Simple harmonic motion is defined as the motion of a particle whose acceleration

is always directed towards the equilibrium point and is directly proportional to the

displacement of the particle from that point. In the experiment, a simple pendulum

will be stuck on the paper tape. the motion of simple pendulum is then investigated.

Procedure:

1. Using a string of length 1.2m,suspend the 0.5 kg ringed mass vertically from the  
 

retort stand-and-clamp.

2. Adjust the position of the clamp so that the mass is about 5 cm above the ground.

3. Cut a ticker-tape of length about 1 m. Write down “Start” on one end and stick that
 

end of the tape to the bottom of the mass.

4. Pass the free end of the tape through the ticker-timer and straighten the tape.

5. Put a cross one the tape at the position just beneath the pin of the ticker-timer to
 

indicate the equilibrium position of the mass.

6.

...read more.

Middle

proportional to the displacement to the fixed point.

8b) a= - k x, where k is a constant

                a is the acceleration of the motion

                x is the displacement of the motion

8c) a , x are directed oppositely and a is directly proportional to x.

8d) For S.H.M., a=-ω²x

8e) v= -Aωsinωt  

a= -Aω²cosωt

9)

When the ringed mass of a simple pendulum is performing an oscillation with small

θ,there is a net restoring force(-mgsinθ).

By Newton's second law, we get:

                        F=ma

                       ma=-mgsinθ

For very smallθ(measured in radians),

So, a=-(g/L)x (since sinθ θ=x/L)

Comparing with a= -ω²x, g/L=ω² and we get that T(period)=2π√(L/g)

10) We have to record the amplitude and the time taken by the mass to travel half of
 

period.

12a) When the simple pendulum starts from the extreme point (amplitude of the

oscillation) ,it's velocity is zero . When it moves towards the equilibrium point, it

accelerates.

...read more.

Conclusion

within 10∘.

Third, we need to ensure the oscillation of simple pendulum is a planar motion,

otherwise, it can not be defined as simple harmonic motion.

Forth, from 12d), we should pay attention that the period of the simple pendulum is

independent of the amplitude. That is, no matter ho the amplitude changes, the period

of the simple pendulum keeps constant.    

Precautions:

1) Ensure the pendulum oscillates with small amplitude(within 10∘).

2) Make sure the pendulum oscillates on the same vertical plane.

3) Use a heavy and small bob in performing the experiment.

4) Measure L to the center of the bob.

Sources of errors:

  1. The amplitude of the oscillation is not small, and it is not a S.H.M. and sinθ=θdoes

not hold.

  1. Buoyancy of the air will reduce down force on mass affect the velocity of the simple

pendulum.

  1. The mass used is not a point mass.

Conclusion:

From the experimental result, we find that the acceleration of the simple pendulum is

always directed towards the equilibrium point and is directly proportional to the

displacement. Therefore, the motion of simple pendulum is simple harmonic, sinusoidal

and independent of amplitude.



   

...read more.

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