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A particle is executing linear simple ha...

A particle is executing linear simple harmonic motion of amplitude A. At what displacement is the energy of the particle half potential and half kinetic?

A

`A/4`

B

`A/2`

C

`A/sqrt(2)`

D

`A/sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
In case of simple harmonic motion,
Kinetic energy, `K = 1/2 momega^(2) (A^(2)-x^(2))`
Potential energy, `U = 1/2 momega^(2)x^(2)`
Total energy,`E = 1/2 momega^(2) A^(2)`
As `U = E/2, therefore 1/2 momega^(2) x^(2) =1/2 [1/2 momega^(2) A^(2)]`
`x^(2) = A^(2)/2` or `x =A/sqrt(2)`
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