what is V(t) before t=0 ? And also, any hints on how to solve the problem. This is not homework. I'm studying for a final exam and I'm really stuck. So if anyone could give me the whole solution for one of the circuits, I would be very thankful.
The method is just like any problem with an ideal diode.
Guess whether the diode is in forward or reverse bias.
Solve the circuit under that assumption.
Check whether the solution actually biases the diode the way you thought.
If it does not, assume the diode is biased the other way, solve again, and check your answer again.
For your circuits you'll have to essentially do this procedure for each switching event in the forcing function (for the \$t<0\$ initial state, for \$0<t<T\$, and for \$t>T\$). For the second circuit, you also have to consider the possibility that the diode changes state during the transient.
As you gain more experience you'll find it gets easier to guess correctly in the first step.
Circuit is at rest before t=0, V(t) = 0 for t<0. You need to solve the circuit for t>0. In first circuit, the diode will be reverse biased for 0 < t < T. So just a simple RC circuit. The battery will charge the capacitor until t=T.
Now for t > T, the battery will be replaced by a short circuit and the diode will be forward biased due to capacitor voltage. Now this will be the discharging circuits.
If you know the equations for charging and discharging of the capacitor, you can solve it easily. There is no difficult and complex circuit analysis involved in it.
Second circuit will be solved in the similar fashion, except that for this time you will need to deal with the inductor and its current.