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The total energy of a particle executing SHM is 80J. What is the potential energy when the particle is at a distance of \frac{3}{}4 of amplitude from the mean position

  • Option 1)

    60 J

  • Option 2)

    10 J

  • Option 3)

    40 J

  • Option 4)

    45 J

 

Answers (1)

best_answer

\\*\frac{U}{E} = \frac{\frac{1}{2}m\omega^{2}y^{2}}{\frac{1}{2}m\omega^{2}a^{2}} = \frac{y^{2}}{a^{2}} \Rightarrow \frac{U}{80} = \left [\frac{\frac{3}{4}a}{a^2} \right ]^{2} = \frac{9}{16} \\*\Rightarrow U = 45\;J

 

Average value of kinetic energy -

Average of kinetic energy

=\frac{\int \left ( K.E. \right )\; dt}{ \int dt}
 

 

- wherein

= \frac{\int \frac{1}{2}m\omega ^{2}A^{2}\cos ^{2}\left ( \omega t+\phi \right )}{\int dt}

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

 

 

 


Option 1)

60 J

This is incorrect.

Option 2)

10 J

This is incorrect.

Option 3)

40 J

This is incorrect.

Option 4)

45 J

This is correct.

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Plabita

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