#### The displacement of an object attached to a spring and executing simple harmonic motion is given by maximum speed first occurs is Option 1) Option 2) Option 3) Option 4)

As we learnt in

Phase constant -

The constant appearing in eqation is called phase constant. It describes initial state.

- wherein

This constant depends on the choice of the instant .

:    Given : displacement  $x= 2\times 10^{-2}\cos \pi t$

$Velocity\: \: \nu = \frac{dx}{dt}= -2\times 10^{-2}\pi \sin \pi t$

$For\: the\: first \: time \: when\: \: \nu = \nu _{max},\sin \pi t= 1$

$or\: \: \: \sin \pi t= \sin \frac{\pi }{2}\: \: \: \: or\: \: \: \: \: \pi t= \frac{\pi }{2}$

$or\: \: \: t= \frac{1}{2}\: \: \: \: s= 0.5s$

Correct option is 2.

Option 1)

This is an incorect option.

Option 2)

This is the correct option.

Option 3)

This is an incorect option.

Option 4)

This is an incorect option.