series-parallel RLC

i need help deriving the second order differential equation for this combination of series and parallel RLC:



i am supposed to end up with one equation...
i can use KVL and KCL to get two equations but i end up with more than 2 variables:

KVL - L*di(L)/dt+ i(R)*R= V in

KCL - i(vin) = i(C) + i(R)
(1/L)*integral of(v(t)) = C*dv(C)/dt + i(R)

how please?

Proceed as follows


iL(t)=iC(t)+iR(t) ---------------(1)

iL(t)=(1/L)∫(Vin-Vout)dt ------(2)

iC(t)=Cd(Vout)/dt -------------(3)

iR(t)=Vout/R ---------------------(4)

Substitute (2), (3) & (4) into (1)

Differentiate through once and you will have your second order equation with Vout as the dependent variable and Vin as the independent.

Would the formula remain the same if a resistor was added in series between the Inductor and the voltage source?

Luke Rodrick said:

Would the formula remain the same if a resistor was added in series between the Inductor and the voltage source?

Click to expand...

If the formula remains the same that means that the resistor has not impact on the output. Does that make sense? Think of it in the extreme in which the resistor is so large in value that it is basically an open circuit. Do you expect the same output voltage as in the original circuit?

WBahn said:

If the formula remains the same that means that the resistor has not impact on the output. Does that make sense? Think of it in the extreme in which the resistor is so large in value that it is basically an open circuit. Do you expect the same output voltage as in the original circuit?

Click to expand...

That does make sense, I was thinking that the general solution would remain the same but now R would be replaced with R thevenin. Which would be the new R in parallel with the R to right. I meant what you said makes sense, not what I said in my original comment.