The maximum velocity of a body in S.H.M. is 0.25 m/s and maximum acceleration is 0.75 $ms^{-2}$, the period of S.H.M. is Option 1) $\frac{\pi}{3}\, \, second$ Option 2) $\frac{\pi}{2}\, \, second$ Option 3) $\frac{2\pi}{3}\, \, second$ Option 4) $\pi\, \, second$

As we discussed in concept

Relation of velocity and displacement -

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

- wherein

$\rightarrow$  x is displacement from mean position

$\rightarrow$  A is Amplitude.

$V_{max}=0.25=Aw$

$a_{max}=0.75=w^{2}A$

$Now \frac{0.75}{0.25}=w =\frac{2\pi }{T}=3$

$T=\frac{2\pi }{3}$

Option 1)

$\frac{\pi}{3}\, \, second$

Option is incorrect

Option 2)

$\frac{\pi}{2}\, \, second$

Option is incorrect

Option 3)

$\frac{2\pi}{3}\, \, second$

Option is correct

Option 4)

$\pi\, \, second$

Option is incorrect

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