Question

A body of mass 0.2kg is executing SHM with amplitude of 20mm. The maximum force which acts upon it is 0.64N
Calculate its maximum velocity and its period of oscillation.
Urgently needed plz someone help me​

Answer 1

Given:

A body of mass 0.2kg is executing SHM with amplitude of 20mm. The maximum force which acts upon it is 0.64N

To find:

• Max Velocity

• Time period

Calculation:

Max force be F :

$\sf \therefore \: F = ma$

$\sf \implies \: F = m \times ( { \omega}^{2} A)$

$\sf \implies \: 0.64 = 0.2 \times ( { \omega}^{2} \dfrac{20}{1000} )$

$\sf \implies \: 3.2 = { \omega}^{2} \dfrac{20}{1000}$

$\sf \implies \: 3.2 = { \omega}^{2} (\dfrac{1}{50} )$

$\sf \implies \: { \omega}^{2} = 3.2 \times 50$

$\sf \implies \: { \omega}^{2} = 160$

$\sf \implies \: \omega = 12.64 \: hz$

So, let time period be t :

$\boxed{ \sf \therefore \: t = \dfrac{2\pi}{ \omega} = \dfrac{2\pi}{12.64} = 0.49 \: sec}$

Let max Velocity be v :

$\boxed{ \sf \therefore \: v = \omega A = 12.64 \times \dfrac{20}{1000} = 0.252 \: m {s}^{ - 1} }$