An Investigation into the factors affecting the time period of a simple pendulum

Tables of results

Mass of Object

Angle of starting

Length of string

Conclusion

I found that the weight of the pendulum did not have any effect on the time needed to complete 50 swings.  This is because the restoring force is equal to the mass multiplied by the acceleration and then the acceleration will therefore be equal to the restoring force divided by the mass.

This means that if the mass is doubled then the restoring force also has to be doubled.  If both of these factors are doubled the acceleration will not be changed and neither will the time the pendulum takes to swing

This is because, as the weight increased, the restoring force also increased, being directly proportional to gravity.  The restoring force then cancelled out the effect of increased weight with the swing time remaining constant.

I also found that the commencement angle had no effect upon the time it took for 50 swings.  Although the pendulum had a larger initial speed, the combined effects of the air resistance and the distance the pendulum had to travel then counteracted this force.  This will have meant that the angle has no effect at all on the time it takes for the pendulum to swing 50 times.

I found it true that the longer the string, the longer time was taken to complete 50 swings.  The diagram shows two pendulums one of which has a length of string which is double the length on the other one.  This shows that the pendulum with a shorter string has a much larger restoring force than the pendulum with the longer string.  

For the shorter stringed pendulum, the acceleration is obviously much larger than the acceleration for the pendulum with the longer string.  As the acceleration is much larger then the time it takes to swing will therefore be much shorter

The graph I made by comparing the length of the string to the time taken shows that the length is equal to the length squared.  The shape of the best-fit line shows this.  This means that the time is proportional to the square root of the length:

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The second graph proves this to be true as the best-fit line is a straight line.  This is proof that there is a definite correlation between the time it takes and square root of the length of the string.

Evaluation

All the results obtained were very good and there were no anomalous readings.

If the acceleration of the pendulum had been uniform throughout it’s movement, then the formula v2=u2+2as should have been able to predict the time it takes for the pendulum to swing.  This was not the case and this proves that the pendulum’s acceleration was not uniform.  This means that another set of formulae would be need to predict the time it takes for the pendulum to swing.

To improve the experiment I could use more accurate ways of reading the results.  First, I could use a protractor, attached to the apparatus which would enable me to measure the angle of the pendulum more effectively.  I could also use a laser centred across the fidutial point.  This beam would be broken whenever the string passed over the point and a computer would be able to accurately count the number of times this has happened.  The computer would also be able to time the swings more accurately as it would stop the timer when the string broke the beam for the final time.

To extend the experiment, I could use more lengths, weights and starting angles.  This would give me much more accurate results.  I could also try to cut out the air resistance acting upon the pendulum by performing the experiments in a vacuum.