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Mechanical Properties of Fluids
Question
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The particle executing simple harmonic motion has a kinetic energy Ko cos2 ωt. The maximum values of the potential energy and the toatal energy are respectively:

  • 0 and 2Ko

  • Ko/2 and K0

  • Ko and 2Ko

  • Ko and Ko

Answer

D.

Ko and Ko

In simple harmonic motion, the total energy of the particle is constant at all instants which are totally kinetic when the particle is passing through the mean position and is totally potential when the particle is passing through the extreme position.

The variation of PE and KE with time is shown in the figure, by the dotted parabolic curve and solid parabolic curve respectively.
Figure indicated that maximum values of total energy KE and PE of SHM are equal.
Now, EK = Ko cos2 ωt
therefore, (EK)max = Ko
So, (EP)max = Ko
and (E)Total  = Ko

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