Final answer:
The period of a simple pendulum is largely independent of the initial angle, especially for small angles, and depends on the length of the pendulum and gravitational acceleration. Unlike simple harmonic oscillators, the pendulum's mass and amplitude have minimal effect on its period.
Step-by-step explanation:
The period of oscillation of a simple pendulum is primarily dependent on two factors: the length of the string and the acceleration due to gravity. It is independent of the mass of the pendulum bob and the maximum displacement or amplitude, especially when the initial angle is less than about 15°. As with simple harmonic oscillators, the period T for a pendulum is nearly independent of amplitude. However, pendulums exhibit anharmonic behavior at larger amplitudes, which can affect the period slightly, but for small angles, the period remains remarkably consistent.
In contrast, a simple harmonic oscillator such as a diving board may have a period that depends on its stiffness (force constant k) and the mass of the system; stiffer systems have shorter periods, and more massive systems have longer periods. This difference underscores the unique characteristics of pendular motion versus other types of oscillating systems.