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  • Need explanation for: - Oscillations and Waves - JEE Main-4

The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement ( amplitude = a) is

  • Option 1)

    \frac{a}{2}

  • Option 2)

    a\sqrt{2}

  • Option 3)

    \frac{a}{\sqrt{2}}

  • Option 4)

    \frac{a\sqrt{2}}{3}

 

Answers (1)

best_answer

Suppose at displacement y from mean position potential energy = kinetic energy

\\*\frac{1}{2}m(a^{2} - y^{2})\omega^{2} = \frac{1}{2}my^{2}\omega^{2} \\*\Rightarrow a^{2} = 2y^{2} \Rightarrow y = \frac{a}{\sqrt{2}}

 

Kinetic energy in S.H.M. -

K.E.= \frac{1}{2}mu^{2}\\ \: \: \: = \frac{1}{2}m\left ( A^{2} -x^{2}\right )\omega ^{2}

 

- wherein

K.E.= \frac{1}{2}K\left ( A^{2}-x^{2} \right ) \\K= m\omega ^{2}

 

 

 


Option 1)

\frac{a}{2}

This is incorrect.

Option 2)

a\sqrt{2}

This is incorrect.

Option 3)

\frac{a}{\sqrt{2}}

This is correct.

Option 4)

\frac{a\sqrt{2}}{3}

This is incorrect.

Posted by

Aadil

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