Derive the expression for the power loss P averaged over a complete steady-state cycle d...

Derive the expression for the power loss P averaged over a complete steady-state cycle due to the frictional dissipation of energy in a viscously damped linear oscillator. The forcing function is and the displacement-time relation for steady-state motion is where the amplitude X is given by Eq. 8/20 (Hint: The frictional energy loss during a displacement is where is the viscous damping coefficient. Integrate this expression over a complete cycle and divide by the period of the cycle.)