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

 

Answers (1)

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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