Question

does the period depend on the amplitude of oscillations?

Answer 1

The equations for Simple Harmonic Motion show that the period is independent of the amplitude of oscillations.

Answer 2

consider a simple pendulum in motion,

The period of oscillations remains constant, while the amplitude will decrease

Answer 3

The time period of the simple pendulum may be treated independent of its amplitude,until the effective length and the amplitude are relatively very very small to the dimensions of the earth.