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  • Help me solve this - Oscillations and Waves - JEE Main-4

A particle executes simple harmonic motion with a frequency f. The frequency with which its kinetic energy oscillates is

  • Option 1)

    \frac{f}{2}

  • Option 2)

    f

  • Option 3)

    2f

  • Option 4)

    4f

 

Answers (1)

best_answer

Kinetic energy K = \frac{1}{2}mv^{2} = \frac{1}{2}ma^{2}\omega^{2}\cos^{2}\omega t = \frac{1}{2}ma^{2}\omega^{2}(1 + \cos 2\omega t)

Hence, Kinetic energy varies periodically with double the frequency of SHM .i.e, 2\omega.

 

Average value of potential energy with respect to t -

Average\: o\! f \\U=\frac{\int v\; dt}{ \int dt}


 

- wherein

\because U= \frac{1}{2}Kx^{2}

average of U

= \frac{\int \frac{1}{2}m\omega ^{2}A^{2}\sin ^{2}\omega t}{\int dt}

= \frac{1}{4}m\omega ^{2}A^{2}

 

 

 


Option 1)

\frac{f}{2}

This is incorrect.

Option 2)

f

This is incorrect.

Option 3)

2f

This is correct.

Option 4)

4f

This is incorrect.

Posted by

Avinash

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