Question

# When particle oscillates simple harmonically its potential energy varies periodically. If frequency of the particle is n, the frequency of the potential energy is

A
n/2
B
n
C
2n
D
4n

Solution

## The correct option is B 2n$$PE=\frac { 1 }{ 2 } m\omega ^{ 2 }x^{ 2 }\\ =\frac { 1 }{ 2 } m\omega ^{ 2 }(x_{ 0 }^{ 2 }\sin ^{ 2 }{ \omega t } )\\ =\frac { 1 }{ 2 } m\omega ^{ 2 }x_{ 0 }^{ 2 }\left( \frac { 1-\cos { 2\omega t } }{ 2 } \right) \\ =\frac { 1 }{ 4 } m\omega ^{ 2 }x_{ 0 }^{ 2 }-\frac { 1 }{ 4 } m\omega ^{ 2 }x_{ 0 }^{ 2 }\cos { 2\omega t }$$frequency of above equation i.e. frequency of P.E. is $$2\omega$$ or $$2n$$Physics

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