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# Determining acceleration of free fall by of a simple pendulum.

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Introduction

Determining acceleration of free fall by of a simple pendulum.

Introduction

In this investigation I am going to use the simple pendulum to determine the value of acceleration of free fall.

The method involves setting pendulums of certain lengths in motion and timing the time taken for ten complete oscillations at that length.

Then using the formula

T = 2π (l/g)

Therefore T2= 4π2l

g

I aim to find the value of acceleration of free fall from the gradient of a graph of T2against l. From the above equation I hope to get a straight line graph with a positive gradient passing through the origin.

As I hope to get a straight line graph the equation of the line will be in the form of

y = mx + c

But since the graph will pass through the origin my c = 0

If the above formula is then re-arranged as follows

T2= 4π2

lg

but T2= gradient for the graphof T2against l

l

Therefore it follows that gradient = 4π2

g

Thus the acceleration of free fall (g) will be given by the equation below

g =     4π2__

My variables are length of pendulum (l), time for oscillations (

Middle

After doing the above process I entered my data in the raw data table below.

Raw data

 Raw data measure Pendulum length (L/m). Uncertainty ± 0.0005 m Time for 10 oscillations (T/s) Uncertainty ± 0.001s Time for 1 oscillations (T/s) Uncertainty ± 0.001s T2 (T/s) Uncertainty ± 0.002s 1 0.95 19.72 1.972 3.89 2 0.90 19.22 1.922 3.69 3 0.85 18.78 1.878 3.53 4 0.80 18.16 1.816 3.30 5 0.75 17.66 1.766 3.12 6 0.70 17.03 1.703 2.90 7 0.65 16.53 1.653 2.73

I then plotted a graph of time2 against length using the values shown in the table above using graphing software. The uncertainty for the length and time are relatively small hence I will ignore them in my graph.

Graph of time squared (T2/s)

Conclusion

• I would like to carry out the procedure of timing the oscillation at different pendulum lengths, for a greater number of times so as to obtain more data whose average I can use in the calculations to obtain a more accurate answer.
• I would also like to time a greater number of complete oscillations when the pendulum bob is set in motion so as to reduce errors that may have arisen due to my reaction time.
• I would also like to carry out the procedure again with a different set of apparatus, so as to eliminate the systematic error that arose in this experiment.
• Finally I would recommend that a heavy mass be placed on the stand holding the pendulum bob, so that it does not dangle when the pendulum bob oscillates thus leading to a more accurate answer.

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