(Solved): Consider the following circuit. The switch is at position A for some long period of time \( t ...

Consider the following circuit. The switch is at position A for some long period of time \( t<0 \). At time \( t=0 \) the switch flips from position A to position B where it remains. Let \( V_{S}=12 u(t), C=100 \mathrm{mF} \), and \( R=10 \Omega \) Using the Laplace transform, find the voltage output \( v_{0}(t) \) across resistor \( \mathrm{R} \) for time \( t \geq 0 \) (Hint: Find the initial condition for \( t<0 \) and then use it to find the output for \( t \geq 0 \) )