# A body is executing simple harmonic motion with a angular frequency $2\; rad/s$. The velocity of the body  at 20 mm displacement when the amplitude of the motion is 60 mm is Option 1) $40\; mm/s$ Option 2) $60\; mm/s$ Option 3) $113\; mm/s$ Option 4) $120\; mm/s$

A Avinash

$v = \omega\sqrt{a^{2} - y^{2}} = 2\sqrt{60^{2} - 20^{2}} = 113 mm/s$

Equation of S.H.M. -

$a=-\frac{d^{2}x}{dt^{2}}= -w^{2}x$

$w= \sqrt{\frac{k}{m}}$

- wherein

$x= A\sin \left ( wt+\delta \right )$

Option 1)

$40\; mm/s$

This is incorrect.

Option 2)

$60\; mm/s$

This is incorrect.

Option 3)

$113\; mm/s$

This is correct.

Option 4)

$120\; mm/s$

This is incorrect.

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