A body is executing SHM when its displacemnt from the mean position is 4cm and 5 cm, the corresponding velocity of the body is 10 cm/s and 8cm/s. Then the time period of the body is  Option 1) $2\pi\;s$ Option 2)  $\frac{\pi}{2} s$ Option 3) $\pi\;s$ Option 4) $\frac{3\pi}{2} s$

$\\*v = \omega\sqrt{a^{2}-y^{2}} \Rightarrow 10 = \omega\sqrt{a^{2}-4^{2}}\;\; and\;\; 8 =\omega\sqrt{a^{2}-5^{2}}$

On solving $\omega =2 \Rightarrow \omega = \frac{2\pi}{T} = 2 \Rightarrow T =\pi \;s$

Relation of velocity and displacement -

$v= w\sqrt{A^{2}-x^{2}}$

- wherein

$\rightarrow$  x is displacement from mean position

$\rightarrow$  A is Amplitude.

Option 1)

$2\pi\;s$

This is incorrect.

Option 2)

$\frac{\pi}{2} s$

This is incorrect.

Option 3)

$\pi\;s$

This is correct.

Option 4)

$\frac{3\pi}{2} s$

This is incorrect.

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