Simple Harmonic Motion.

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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:

The results are as follows:

The graph of T againstis drawn on a separate graph paper and is attached on the next page (page 4).



Data analysis:

From the graph, it is easily observed that the relation between T and is linear as the points are nearly in a straight line.

The x-coordinate of the centroid of the three points =

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Percentage error =

The y-coordinate of the centroid of the three points =

Percentage error =

The slope of the best fit =

Percentage error = 2.86 + 2.84% = 5.70%

Absolute error =

 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:

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