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A linear harmonic oscillator has a total...

A linear harmonic oscillator has a total mechanical energy of `200 J`. Potential energy of it at mean position is `50J`. Find
(i) the maximum kinetic energy,
(ii)the minimum potential energy,
(iii) the potential energy at extreme positions.

Text Solution

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(i) At mean position , potential energy is minimum .
Hence, `U_("min")=50J`
(ii) At mean position , KE is maximum
`therefore K_("min")=E-U_("min")=200-50=150 J`
(iii) At extreme positions, kinetic energy is zero and potential energy is maximum
`therefore U_("min")=E=200 J`
`" "` (From law of conservation of energy)
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