A particle starts oscillating simple harmonically from its equilibrium position then, the ratio of kinetic energy and potential energy of the particle at the time `T//12` is: `(T="time period")`

Options

A. `1 : 4`
B. `2 : 1`
C. `3 : 1`
D. `4 : 1`

Answer

C

Explanation

When `t = (T)/(12)`, then `x = A "sin"(2pi)/(T)xx(T)/(12)=(A)/(2)`
`KE = (1)/(2)mv^(2)=(1)/(2)m omega^(2)(r^(2)-x^(2))`
`= (1)/(2)m omega^(2)(A^(2)-(A^(2))/(4))`
`=(3)/(4)((1)/(2)momega^(2)A^(2))`
`PE = (1)/(2)m omega^(2)x^(2)=(1)/(4)((1)/(2)m omega^(2)A^(2))`
`(KE)/(PE)=(3)/(1)`