Question

A body vibrate in simple harmonic motion with a frequency of 50hz and an amplitude of 4cm. Find

1.period

2. Acceleration at the middle and at the end of the path of oscillation

Answer 1

1.

The period of oscillations

$$T=\frac{1}{f}=\frac{1}{50\rm\: Hz}=0.02\:\rm s$$

2.

The acceleration at the middle point is zero.

The acceleration at the end point is equal

$$a_{\max}=A\omega^2=4\pi^2Af^2\\ =4\times 3.14^2\times0.04\;\rm m\times (50\: Hz)^2=3944\: m/s^2$$