Due to the external vertical force `F_(x)=F_(0)cos omegat ` a body suspended by a spring performs forced steady `-` state oscillations according to the law`x=a cos( omega t - varphi)`. Find the work performed by the force `F` during one oscillation period.

Explanation

The work doen in one cylcle is
`A= int F dx= int _(0)^(T)F v dt=int _(0)^(T) F_(0)cos omegat( - omega a sin ( omega t - varphi)) dt `
`=int_(0)^(T)F_(0) omega a ( - cos omega t sin omega t cos varphi + cos ^(2) omega t sin varphi ) dt `
`=(1)/(2) F _(0) omega a (T)/(2) sin varphi = pi a F_(0) sin varphi `