Question

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")`

Answer 1

At,`t=(T)/(12),x A "sin" (2pi)/(T)xx(T)/(12)=A"sin"(pi)/(6)=(A)/(2)`
so, KE`=(1)/(2)k(A^(2)-x^(2))=(3)/(4)xx(1)/(2)kA^(2)`
and `PE=(1)/(2)kx^(2)=(1)/(4)xx(1)/(2)kA^(2)`
`therefore (KE)/(PE)=(3)/(1)`