Pendulum

Period: time taken for one complete oscillation.

One complete oscillation: one complete to-and-fro motion, like A -> B -> C -> B -> A
Period of pendulum affected by  
    (1) Length of pendulum, l 
    (2) Gravitational field strength, g
It is not affected by
    (1) Mass of pendulum bob
    (2) Angle of release

Note that the period of pendulum is indeed affected by the angle of release, but by a very small amount. Therefore, to minimize this, we normally release the pendulum with an angle less than 10 deg such that it wont affect the period of pendulum. This means whenever we talk about angle of release for pendulum, we assume it is a small angle. Also, note that the formula stated above is only valid for small angle of release.

These factors can be analyzed with the applet below. Detailed steps to analyze each factor are found below the applet.
Steps in analyzing mass of pendulum bob factor:
1) Make sure 1st pendulum has a length of 2.0 m and mass of 1.0 kg.
2) Select "show 2nd pendulum" and change the length to 2.0 m and mass to 0.5 kg.
3) Select "photogate timer" found at the bottom right and keep the rest untouched. This will show us the period of pendulum.
4) Displace the 1st pendulum to an angle of 10 deg and release; Likewise for 2nd pendulum.
5) Now, start the photogate timer for 1st pendulum and take down the timing, t1.
6) Click pendulum 2 on photogate timer interface and start. The timing now should be same as t1. So we can conclude that the period of pendulum does not depend on the mass of pendulum bob.
Steps in analyzing Gravitational Field Strength factor:
1) Click "Reset" button.
2) Make sure the pendulum has a length of 2.0 m and mass of 1.0 kg.
3) Unselect "show 2nd pendulum".
4) Make sure Earth is selected.
5) Select "photogate timer" found at the bottom right and keep the rest untouched. This will show us the period of pendulum.
6) Displace the pendulum to an angle of 10 deg and release.
7) Now, start the photogate timer and take down the timing, t1.
8) Select "Moon" to change the gravitational field strength and start the photogate timer again. You should see that the timing now is much longer than t1 as gravitational field strength on Moon is smaller than that on Earth. So we can conclude that the period of pendulum is affected by the gravitational field strength.
Steps in analyzing angle of release factor:
1) Click "Reset" button.
2) Make sure 1st pendulum has a length of 2.0 m and mass of 1.0 kg.
3) Select "show 2nd pendulum" and change the length to 2.0 m and mass to 1.0 kg.
4) Select "photogate timer" found at the bottom right and keep the rest untouched. This will show us the period of pendulum.
5) Displace the 1st pendulum to an angle of 5 deg and release; Likewise for 2nd pendulum but with an angle of 10 deg.
6) Now, start the photogate timer for 1st pendulum and take down the timing, t1.
7) Click pendulum 2 on photogate timer interface and start. The timing now should be same as t1. So we can conclude that the period of pendulum does not depend on the angle of release.
Steps in analyzing Length of Pendulum factor:
1) Click "Reset" button.
2) Make sure 1st pendulum has a length of 2.0 m and mass of 1.0 kg.
3) Select "show 2nd pendulum" and change the length to 1.0 m and mass to 1.0 kg.
4) Select "photogate timer" found at the bottom right and keep the rest untouched. This will show us the period of pendulum.
5) Displace the 1st pendulum to an angle of 10 deg and release; Likewise for 2nd pendulum.
6) Now, start the photogate timer for 1st pendulum and take down the timing, t1.
7) Click pendulum 2 on photogate timer interface and start. The timing now is shorter than t1. So we can conclude that the period of pendulum is affected by the length of pendulum.
Excel@Physics