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=VmeβtcosωtV=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.

Reveal Answer
4.101. (a) tn=πnωt_{n}=\frac{\pi n}{\omega}; (b) tn=1ω[arctan(βω)+πn]t_{n}=\frac{1}{\omega}\left[\arctan \left(-\frac{\beta}{\omega}\right)+\pi n\right] \cdot Here n=0,1,2,n=0,1,2, \ldots