This experiment was carried out to investigate the factors that affect the period of a pendulum.

A pendulum is a weight hung from a fixed point so that it can swing freely. The total energy throughout

the movement of the pendulum remains constant. At its highest point, it has its maximum potential

energy and no kinetic energy. As it begins to fall, the potential energy begins to change into kinetic

energy until it reaches its lowest point where the kinetic energy is at a maximum and the potential

energy is equal to zero. When it begins to rise again the kinetic energy begins to change potential energy

until it reaches its maximum once again at the highest point.

A pendulum moves back and fro due to gravity. When the mass is drawn upwards and let go, the

force of gravity accelerates it back to the original position. The momentum built up by the acceleration

of gravity causes the mass to then swing in the opposite direction to a height equal to the original

position. This force is called inertia: (its tendency to resist its state of motion.)

It was shown that the length of the string affected the period of a pendulum. This was displayed in the results as the different times taken for 20 oscillations whilst changing the length of the string varied from 12.60 to 30.90 seconds. Meanwhile the times calculated for one oscillation varied from 0.63 to 1.54 seconds. Here the reasoning behind this finding. An object on a pendulum with a long string is further away from the axis of the pendulum. This means that it has to cover a longer distance to return to where it came from. This is the case since a longer radius from the axis of rotation means a longer arc length for the bob to travel along. The formula linking the length of the string to the period of the pendulum is seen below:

𝑇 = 2𝜋√𝑙𝑔

Where ‘T’ is the period, ‘l’ is the length of the string and ‘g’ is the gravitational field strength.

The mass of the bob doesn’t affect the period of the pendulum since the movement is due to

gravity. Acceleration due to gravity is a constant figure( 9.8 ms -2) and no matter how heavy the bob is,

the pendulum will accelerate at this rate and take the same amount of time to complete one back and

fro movement. As shown in the experiment, the time taken for 20 oscillations only varied from 24.10 to

25.18 seconds. This variation in the results is only to due the random error and the vary reaction times

to measure the oscillations. The times calculated for one oscillation with varying masses also had a small

range from 1.21 to 1.26 seconds.

Finally the angle of displacement was tested and results showed that this factor doesn’t really

affect the period of a pendulum. Times for 20 oscillations recorded at different angles varied only from

21.65 to 22.65 seconds whilst the time calculated for one oscillation range from 1.08 to only 1.13

seconds. When the angle of displacement increases, the starting height of the bob is higher thus it will

accelerate over a longer period and gain a greater velocity. However, this movement is over a longer

distance, so the time taken for one oscillation will not decrease. It will remain constant.

It was advisable to divide the results by 20 to reduce random error due to human reaction time.

Sources of Error

Sources of Error:

- The time for one oscillation was slightly inaccurate as friction due to air resistance slows the

pendulum down with each swing.

- The time for twenty oscillations was slightly inaccurate due to the time taken (human

reaction time) to start and stop the watch.

- There was uncertainty in the reference point at which to start and the stop the watch.

- There was a bit of uncertainty about which point of swing to time.

Precautions

- The time taken for 20 oscillations was divided by 20 to reduce the error due to human

reaction time.

- All windows were closed to ensure that the force of the wind did not affect the movement

of the pendulum.