All Problems Electric Oscillations
Problem 4.101
The free damped oscillations are maintained in a circuit, such that the voltage across the capacitor varies as \(V=V_{m} e^{-\beta t} \cos \omega t\). Find the moments of time when the modulus of the voltage across the capacitor reaches (a) peak values; (b) maximum (extremum) values.
4.101. (a) \(t_{n}=\frac{\pi n}{\omega}\); (b) \(t_{n}=\frac{1}{\omega}\left[\arctan \left(-\frac{\beta}{\omega}\right)+\pi n\right] \cdot\) Here \(n=0,1,2, \ldots\)