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# Simple Harmonic Motion.

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Introduction

Physics Practical Report

Title:        Simple Harmonic Motion

Objective:        To examine the characteristics of the motion of a simple pendulum and measure the gravitational acceleration g.

Apparatus:        One approximately 0.5 kg mass, one G-clamp, one long string, one ticker-timer, one roll of ticker tape, one low voltage power supply, one stand and clamp, two chairs, one stop watch.

## Theories:

In a simple harmonic motion, it is defined that .

The displacement is defined as , where A is the amplitude, is the angular velocity and t is time of the motion.      Hence, when x is at equilibrium position, a must be zero.

In a simple pendulum,

F        =  mgsinθ

ma        =  mgsinθ

a        =  gsinθ

If θ is very small, sinθ = θ when measured in radian.

a        ≈  gsinθ

=  (-g)( )  and     Hence, the slope found is – .

Furthermore,    The slope of a T- graph is .

SETUP 1:

We have set up a simple pendulum by using an approximately 0.5kg mass, a G-clamp, one chair, a string and a stand and clamp as follow:

Procedures:

We then set the pendulum into motion with different lengths l of string and use a stop watch to record the period (T). 10 periods (10T) of the motion is recorded for each length of string (l).

Measurements:

Middle  The slope of the best fit = .

The theoretical slope = .

Hence, the experiment is done quite accurately.

SETUP 2:

We have then modified the simple pendulum a little by connecting it with a ticker-timer system to record the motion of the simple pendulum as shown below:

Procedures:

With the attachment of a ticker-tape, we set the mass at rest in the vertical position and mark down the equilibrium position on the tape. We then pull the mass to the right. After that, we turn on the power supply and allow the ticker-timer to take position-time record on ticker tape. We then immediately release the mass and allow it to swing to left. When the mass was completely swung to the left, we turned off the power supply to prevent any unwanted tick on the ticker tape.

Observations: The frequency of the ticker-timer is 50Hz.

T  =  The time interval between two successive dots        = = 0.02s

It is obvious to see that the separation between two successive dots before reaching the equilibrium position increases but decreases after reaching the equilibrium position.

Take the direction to the right is positive.

At t = 0, the displacement is maximum, the velocity is zero and the acceleration is negatively maximum.

Conclusion

Moreover, we observed that the mass would rotate a little itself. This error is very difficult to prevent from unless an extremely care is paid when performing the experiment. Again, some energy may be converted from translational energy to rotational energy. Hence, the speed would be slower.

One more error is the air resistance. There may be damping forced added onto the system. This may reduce the speed of the mass.

## Precaution

The clamp should not oscillate despite the fact that the arm of the stand is not strictly held on the base.

The whole stand and clamp should be held firmly by G-clamp.

The angle of oscillation should be small. Otherwise, the assumption does not hold.

The equilibrium position should be marked accurately so that the period is correct.

The mass should be released skillfully so that the mass does not move in an ellipse form and does not move circularly itself.

Page

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