So far I' ve calculated vc(0+)= -12 V and il(0+)= 0 A, but I really don't know how to get to the differential equation for vo(t) for t>0. I do not really understand where to apply KCL or KVL or how to even start. I would really appreciate your help. Thanks!

 

Your initial conditions are only partly specified. Voltages and currents are both signed quantities, and so the reference directions must be clearly defined. While I can guess what the reference polarity of your capacitor voltage probably is, engineering is not about guessing, so don't make your readers (which, by the way, includes the person grading your work) guess. But as for the inductor current, I haven't got a clue what your reference direction is.

Best policy is that any quantity that you make use of, annotate it on your diagram to include the reference direction. Notice that they didn't just ask you to find the voltage across the leftmost 6 ohm resistor, they annotated it, including its reference direction, directly on the diagram.

If you are to the point of working with second order transient circuits, then is it safe to assume that you know how to do nodal voltage and mesh current analysis? If so, then set up the equations as best you can and present them here so that we can look them over.

 

Where can you simplify the circuit by substituting a Thevenin equivalent?

 

Where can you simplify the circuit by substituting a Thevenin equivalent?

Good suggestion. Given the point where they are asking for the response at, I wouldn't be surprised if they specifically intended for people to reduce part via Thevenin.

 

So far I' ve calculated vc(0+)= -12 V and il(0+)= 0 A, but I really don't know how to get to the differential equation for vo(t) for t>0. I do not really understand where to apply KCL or KVL or how to even start. I would really appreciate your help. Thanks!View attachment 137424

Hi,

Quick question:
What have you done in the past that you think might help in this circuit?
Have you already done RC and RL circuits for example, and with initial conditions too?
This could help others here help you faster and easier.