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

 

Answers (1)
A Aadil Khan

\\*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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