Final answer:
The period of a simple pendulum is determined by its length and the acceleration due to gravity, and is independent of the pendulum bob's mass. This is due to the cancelling out of gravitational force and inertia in the pendulum's motion.
Step-by-step explanation:
The period of oscillation of a simple pendulum is given by the formula T = 2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. This formula shows that the period T is independent of the mass of the pendulum bob. The reason for this is that the gravitational force acting on the mass and the mass's inertia, cancel each other out in the harmonic motion of a pendulum, leading to a period that depends only on l and g.
The fact that the period of a pendulum is independent of mass can be counterintuitive but allows pendulums to be used for measuring gravitational acceleration in different locations. Importantly, this relationship holds true as long as the amplitude of the pendulum's swing is relatively small (usually less than about 15°).