It depends on the pendulum. In the case of simple, or mathematical, pendulum, the period does not depend on the mass. The simple pendulum is a small massive ball hanging on a long string (that is, the size of the ball is very small compared to the length of the string.) The period of such pendulum depends only on the length of the string and the gravitational acceleration:
`T = 2pisqrt(l/g)` .
This period can change only if the length of the string changes or if it the pendulum is placed somewhere where gravity is different, such as on the Moon. The mass of the ball will not affect the period.
When the ball, or any other object is large enough so that its size cannot be neglected, it becomes a physical pendulum. The period of the physical pendulum is more complicated:
`T = 2pisqrt(I/(mgl))`
Here, I is the moment of inertia of the oscillating object, m is the object's mass, and l is the distance from its center of mass to the pivot. In this case, the increase of mass might affect the period, depending on how the moment of inertia of the object changes due to the change in mass.
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