The free damped oscillations are maintained in a circuit, such that the voltage across the capacitor varies as `V=V_(m)theta^(betat) cos omegat `, Find the moments of time when the modulus of the voltage across the capacitor reaches
`(a)` peak values,
(b) maximum ( extremum ) values.

Explanation

Given `V=V_(m)e^(-betat) cos omegat`
`(a)` The phrase `'` peak values `'` is not clear. The answer is obtained on taking `|cos omega t|=1`
`i.e. ` `t=(pin)/(omega).`
`(b)` For extrema `(dV)/(dt)=0`
`- beta cos omegat- omega sin omega t =0`
or ` tan omegat =- beta // omega`
`i.e.` ` omegat=n pi + tan ^(-1)((- beta)/( omega))`.