So, let's say we have a series LC circuit with generator ug(t)=Um*cos(ωt)

Then the output signal would be (if we consider the current in the circuit as the output signal) :

Now, basically i can understand what happens up to this moment, where

**i don't understand why angle is 90 degrees if frequency of the circuit is lower than the one of the generator and -90 degree otherwise**. Now, there's a special case after this. What happens when frequency of the circuit is the same as the frequency of the generator? It then says that we cannot find the solution using complex numbers representations of the values in circuit since transfer function (i believe that's the correct term for the "output over input" function) reaches infinity in this case, so instead, particular solution to the differential equation of this circuit has looks something like this:

**Why would the response to excitation look like this**(since i know for the three types only, and none of them fits this)?

So i don't know how to find the response in this circuit in case of resonance. Any help appreciated!