(Solved): For the underdamped circuit shown in Fig. P7.110, determine the voltage \( v(t) \) if the initial ...

For the underdamped circuit shown in Fig. P7.110, determine the voltage \( v(t) \) if the initial conditions on the storage elements are \( i_{L}(0)=4 \mathrm{~A} \) and \( v_{C}(0)=20 \mathrm{~V} \). Figure P7.110 \[ \begin{array}{l} v(t)=e^{-4 t}[\cos (2 t)+120 \sin (2 t)] V \\ v(t)=e^{-4 t}[120 \cos (2 t)-20 \sin (2 t)] V \\ v(t)=e^{-4 t}[20 \cos (2 t)-120 \sin (2 t)] V \\ v(t)=e^{-2 t}[20 \cos (4 t)-120 \sin (4 t)] V \end{array} \] Question 4 2 pts Find \( V_{c}(t) \) for \( t>0 \) in the circuit in Fig. \( P 7.111 \) if \( v_{c}(0)=0 \). Figure P7.111 \[ \begin{array}{l} \mathrm{V}_{\mathrm{c}}(\mathrm{t})=8.34 \mathrm{e}^{-260.152 \mathrm{t}}-0.34 \mathrm{e}^{-6406.52 \mathrm{t}}-8 \mathrm{~V}, \mathrm{t}>0 \\ \mathrm{~V}_{\mathrm{c}}(\mathrm{t})=-8.34 \mathrm{e}^{260.152 \mathrm{t}}+0.34 \mathrm{e}^{-6406.52 \mathrm{t}}+8 \mathrm{~V}, \mathrm{t}>0 \\ \mathrm{~V}_{\mathrm{c}}(\mathrm{t})=8.34 \mathrm{e}^{-260.152 \mathrm{t}}+0.34 \mathrm{e}^{-6406.52 \mathrm{t}}+8 \mathrm{~V}, \mathrm{t}>0 \\ \mathrm{~V}_{\mathrm{c}}(\mathrm{t})=-8.34 \mathrm{e}^{-260.152 \mathrm{t}}+0.34 \mathrm{e}^{-6406.52 \mathrm{t}}+8 \mathrm{~V}, \mathrm{t}>0 \end{array} \]