Question

A 2.5 kg mass undergoes SHM and makes exactly 3 vibrations each second. Compute the acceleration and the restoring force acting on the body when its displacement from the equilibrium position is 5.0cm.​

Answer 1

Given, mass of body = 2.5 kg and displacement = 0.05 m

Number of vibrations in one second is called frequency.

Here, frequency = 3 Hz

Time period = 1/frequency = 1/3 s

Time period (T) = 2π/w

w = 2π/T

w = 2π/(1/3)

w = 6π

(w = angular frequency).

For a particle moving in SHM,

acceleration = - w²x (X is displacement).

acceleration = -36π²×0.05

Taking π² = 10 nearly.

acceleration = -36 × 10 × 0.05 = - 18 m/s²

negative sign represents that acceleration and displacement are in opposite direction.

Restoring force = mass × acceleration

= 2.5 × 18

= 45 N

Hope, this helps you