The following series $\text{RLC}$ circuit with zero initial conditions is excited by a unit impulse function $\delta(t)$.
For $t>0$, the output voltage $V_{c}(t)$ is
- $\frac{2}{\sqrt{3}}\left(e^{-\frac{1}{2} t}-e^{-\frac{\sqrt{3}}{2} t}\right)$
- $\frac{2}{\sqrt{3}} t e^{-\frac{1}{2} t}$
- $\frac{2}{\sqrt{3}} e^{-\frac{1}{2} t} \cos \left(\frac{\sqrt{3}}{2} t\right)$
- $\frac{2}{\sqrt{3}} e^{-\frac{1}{2} t} \sin \left(\frac{\sqrt{3}}{2} t\right)$