The displacement of a particle varies according to the relation $x=4\left ( \cos \pi t+\sin \pi t \right )$ . The amplitude of the particle is

Option 1)
$-4$

Option 2)
$4$

Option 3)
$4\sqrt{2}$

Option 4)
$8$

Answers (1)

P perimeter

As we learnt in

Equation of S.H.M. -

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

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

- wherein

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

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

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

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)

$-4$

The is an incorrect option.

Option 2)

$4$

The is an incorrect option.

Option 3)

$4\sqrt{2}$

This is the correct option.

Option 4)

$8$

The is an incorrect option.

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

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The displacement of a particle varies according to the relation $x=4\left ( \cos \pi t+\sin \pi t \right )$ . The amplitude of the particle is

Option 1)
$-4$

Option 2)
$4$

Option 3)
$4\sqrt{2}$

Option 4)
$8$