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

Answer

A

Explanation

As the particle starts its motion from the equilibrium position, so
`x=Asinomegat=Asin.(2pi)/(T)t,"At "t=(T)/(12),x=Asin.(2pi)/(T)xx(T)/(12)=(A)/(2)`
`therefore` Kinetic energy, `K=(1)/(2)momega^(2)(A^(2)-x^(2))=(1)/(2)momega^(2)(A^(2)-(A^(2))/(4))`
`=(3)/(4)((1)/(2)momega^(2)A^(2))`
and potential energy, `U=(1)/(2)momega^(2)x^(2)=(1)/(2)momega^(2)((A)/(2))^(2)`
`=(1)/(4)((1)/(2)momega^(2)A^(2))`
Thus, `(K)/(U)=(3)/(1)`