Question

Why is pendulum period independent of mass?

Answer 1

Fundamentally, the reason mass is absent from the pendulum equation is because the force that drives the oscillation of the pendulum is gravity. ... The combination of these two things causes the mass to cancel out of the equation, and so the motion of a pendulum is independent of the mass of the pendulum bob.

Answer 2

Acceleration due to gravity is same for all masses. So downward movement of pendulum is going to be same for all masses. Similary deceleration due to gravity will be same so time of acent is going to be same too.