#### A point mass oscillates along the x -axis according to law . If the acceleration of the particle is written as then 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 :$x= x_{0}\cos \left ( \omega t-\frac{\pi }{4} \right )\cdots \cdots \cdots (i)$

$Acceleration\: \: a= A\: \cos \left ( \omega t +\delta \right )\cdots \cdots (ii)$

$Velocity\: \: \nu = \frac{dx}{dt}$

$\nu = -x_{0}\omega \sin \left ( \omega t-\frac{\pi }{4} \right )\cdots \cdots \cdots (iii)$

$Acceleration\: \: a= \frac{d\nu }{dt}$

$= x_{0}\omega ^{2}\cos \left [ \omega t+\frac{3\pi }{4} \right ]$

$Compare \: \: (iv)\: \: with\: \: (ii),\: \: we\: \: get$

$A= x_{0}\omega ^{2},\delta = \frac{3\pi }{4}$

Correct option is 1.

Option 1)

This is the correct option.

Option 2)

This is an incorrect option.

Option 3)

This is an incorrect option.

Option 4)

This is an incorrect option.