A particle of mass `m` excuting `SHM` make `f` oscillation per second. The difference of its kinetic energy when at the centre, and when at distance x from the centre is

Options

A. `pi^(2)f^(2)x^(2)m`
B. `2pi^(2)f^(2)x^(2)m`
C. `(1)/(2)pi^(2)f^(2)x^(2)m`
D. `f^(2)x^(2)m`

Answer

B

Explanation

`KE` at centre
`= 1/2 momega^(2)(A)^(2) = 1/2m4pi^(2)f^(2)A^(2)`
KE at distance `x`
`= 1/2 m4pi^(2)f^(2)(A^(2) - x^(2))`
Difference `= 1/2 m xx 4pi^(2)f^(2)x^(2) = 2pi^(2)f^(2)x^(2)m`