Carry out an experiment of simple harmonic motion using a simple pendulum and determine the acceleration due to gravity, to verify the equation T = 2PÖ(l/g) and show the relationship between time period and length.

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SIMPLE HARMONIC MOTION AND THE SIMPLE PENDULUM

Task 1

Aim

To carry out an experiment of simple harmonic motion using a simple pendulum and determine the acceleration due to gravity, to verify the equation T = 2Π√(l/g) and show the relationship between time period and length.

Method

The apparatus is set up, as above, the string must be measured carefully with a ruler to minimise any error; the length should start off fairly short at about 0.2m for example.  The bob should be secure.

A table should be made for results, this should include length, time (twice), average time and time period (= average time/20).

The pendulum is set into motion by a gentle push, some practice in doing this and also counting and timing the oscillations beforehand may help to achieve greater accuracy.

The angle of amplitude should be kept similar if not the same for each experiment, to make sure the forces acting on it are the same.

It is easier to count the oscillations from the equilibrium position as this is where the pendulum has no energy.  

The number of oscillations counted should be about 20 as it is easier to count a larger number.  The reaction time needed to count one single oscillation would be so small that errors could easily occur.

The timing for 20 oscillations should be repeated to calculate an average time.

The string is now adjusted and measured for a longer length, about an extra 10cm.

The experiment is repeated 6 more times, with the length of string being increased by 0.1m.

The force of gravity is constant, whereas the length and the time period are variable.

Therefore the equation for the time period - T = 2(L/g)  can be re arranged and compared to the equation of a graph – y = m x + c.

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Where: T = Time period

          L = Length

          g = gravity

y and x are always the variables, and m and c are the constants.  

Since gravity is the constant, a value for the acceleration due to gravity can be determined from the gradient.

T = 2Π  x √L

      √g                  

                  

y =  m       x  + c

 Where  m ...

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