period switch question..

[transgalactic]

https://i39.tinypic.com/snea2v.gif

i tried to connect the dots here:
Vc1(0-)=1
Vc2(0-)=4

kvl:
-Vc1-L(I')-Vc2=0

i need to have a second order diff equation
so I=C(Vc') the currect is equal on every capacitor =>I=4(Vc1')

so i have
-Vc1-L((4(Vc1'')-Vc2=0

now i have two uknowns
and i cant say Vc1=Vc2 because there is an inductor in the middle
and i cant say that the inductor acts as a short circuit
because we are not at t->infinity
so i dont know how to solve this equation.

and this is only a small part of the big problem

i dont know what to do when the switch is open
there is no equation the could be done.

i dont know how to find the stored energy
i dont know how to find state trajectory
??

 

[MrAl]

Hi,

Didnt you learn how to work with second order differential equations, or
some other way to analyze circuits that have second order responses like this
yet? If not, you should probably review that first. Just wondering where
you are getting all these problems from and why you are trying to solve them?


You should know how to calculate the stored energy at t=0 right?
The stored energy at t=2*pi changes of course and they are asking you
to take a look at that and see what significance the time t=2*pi has, if any.
After you are able to analyze the circuit for the states iL and vC you can
then easily graph the state trajectory in the iLvC plane, and i might add that
it is interesting to look at this trajectory from 0 to 4*pi instead of just 0 to 2*pi.

Does it help if you lump the two caps into one Cx with Cx=C1+C2 and apply
the initial conditions of 5v with a battery in series?