The equation of a body of mass m and performing a linear S.H.M is given by `x = a "sin" omega t + b "sin" (omega t +(pi)/(2))`. The total energy of the particle at any ins"tan"t is

Options

A. `(1)/(2)momega^(2)ab`
B. `((1)/(2)momega^(2))/(sqrt(a^(2)+b^(2)))`
C. `(1)/(2)m omega^(2)(a^(2)+b^(2))`
D. `(1)/(2)momega^(2)sqrt(a^(2)+b^(2))`

Answer

C

Explanation

The amplitude of S.H.M. `A=sqrt(a^(2)+b^(2))`
`therefore " Total energy " E=(1)/(2)m omega^(2)A^(2)=(1)/(2)m omega^(2)(a^(2)+b^(2))`