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.

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