The time period of a simple pendulum which is oscillating is given by the following equation:
`T = 2pi sqrt(L/g)`
where, T is the time period of oscillations, L is its length and g is the acceleration due to gravity.
Thus, the time period is directly proportional to the square root of the pendulum length. That is,
`T alpha sqrtL`
This means that in order to increase the time period of a simple pendulum, we have to increase its length. If the length of the pendulum is increased by a factor of 4, the time period increases by a factor of 2.
That is, `T' alpha sqrt(L')`
`T' alpha sqrt(4L)`
`T' alpha 2sqrt(L)`
`T' = 2T`
The change in the mass of a pendulum will not have any effect on the time period of the pendulum.
Thus, pendulum length is the only variable on which the time period of a simple pendulum depends.
Hope this helps.