Problem 4.103

A circuit with capacitance \(C\) and inductance \(L\) generates free damped oscillations with current varying with time as \(I\) \(=I_{m} e^{-\beta t^{2}} \sin \omega t .\) Find the voltage across the capacitor as a function of time, and in particular, at the moment \(t=0\).

Reveal Answer

\begin{aligned} &\text { 4.103. } V_{C}=I_{m} V \overline{L / C} \mathrm{e}^{-\beta t} \sin (\omega t+\alpha) \text { with } \tan \alpha=\omega / \beta ; V_{C}(0)=\\ &=I_{m} \sqrt{\frac{L}{C\left(1+\beta^{2} / \omega^{2}\right)}} \end{aligned}

Electric Oscillations