# The displacement of a particle varies according to the relation . The amplitude of the particle is Option 1) Option 2) Option 3) Option 4)

As we learnt in

Equation of S.H.M. -

- wherein

$:x= 4\left ( \cos \pi t+\sin \pi t \right )$

$= 4\times \sqrt{2}\left [ \frac{1}{\sqrt{2}}\cos \pi t+\frac{1}{\sqrt{2}} \sin \pi t\right ]$

or        $x= 4 \sqrt{2}\left [ \sin \frac{\pi }{4}\cos \pi t+\cos \frac{\pi }{4} \sin \pi t\right ]$

$= 4 \sqrt{2}\sin \left ( \pi t+\frac{\pi }{4} \right )$

$Hence\: \: amplitude \: \: = 4\sqrt{2}$

Correct option is 3.

Option 1)

The is an incorrect option.

Option 2)

The is an incorrect option.

Option 3)

This is the correct option.

Option 4)

The is an incorrect option.

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