Question

A body of mass 0.8 kg performs linear S.H.M. It experiences a restoring force of 0.4 N when its displacement from the mean position is 4 cm. Determine the force constant and period of S.H.M.

Answer 1

Given:

Mass of the body (m) = 0.8 kg

Restoring force (F) = 0.4 N

Displacement from mean position (x) = 4 cm = 4 × 10⁻² m

Calculations:

1. Calculate Force Constant (k): 

Using Hooke’s Law,

F = −kx

`k = F/x`

`k = 0.4/(4 xx 10^-2)`

k = 10 N/m

2. Calculate Period of S.H.M. (T):

`T = 2 pi sqrt(m/k)`

`T = 2 pi sqrt(0.8/10)`

T = 2π × 0.2828

T = 1.78 s