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 `(2 pi )/(T) xx ( T) /(12) = (A)/(2)`
KE = `(1)/(2) mv^(2) = (1)/(2) momega^(2) ( A^(2) -x^(2))`
`= (1)/(2) m omega^(2) ( A^(2) - (A^(2))/(4))`
`= (3)/(4) ( (1)/(2) m omega^(2) A^(2))`
PE `= (1)/(2) m omega^(2) x^(2) = (1)/(2) ((1)/(2) m omega^(2) A^(2))`
`(KE)/(PE) = (3)/(1)`
Hence, the required ratio is 3 : 1