Question

A body vibrating with simple harmonic motion has a frequency of 4Hz and an amplitude of 0.15m.
Calculate
1. The maximum values of the acceleration and velocity
2. The acceleration and velocity at a point 0.09m from the equilibrium position of motion

Answer 1

1.

$$a_{max}=(2\pi f)^2A=(2(4)\pi)^2 0.15=95 m/s^2$$

$$v_{max}=(2\pi f)A=(2(4)\pi) 0.15=3.8 m/s$$

2.

$$a=(2(4)\pi)^2 0.09=57 m/s^2$$

$$v=(2(4)\pi) 0.09=2.3 m/s$$