Final answer:
The period of a simple pendulum, given by T = 2π √(l/g), is independent of mass because mass factors cancel out in the forces involved. It is also nearly independent of amplitude, especially if less than 15 degrees, which allows simple pendulum clocks to be accurate timekeepers.
Step-by-step explanation:
The period of a simple pendulum is determined by the equation 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 equation indicates that the period is independent of the mass of the pendulum. The reason the mass of the ball in the pendulum does not affect the period is due to the way gravitational force and the restoring force in a pendulum operate. Both of these forces are proportional to the mass of the object, which means mass factors cancel out when calculating the period.
An important aspect to consider is that the period of the pendulum is nearly independent of amplitude (the maximum displacement), especially if the amplitude is less than about 15 degrees. This, in combination with its mass independence, makes the simple pendulum a reliable timekeeping device when finely adjusted, as even simple pendulum clocks can remain accurate.