Calling the variable voltage source voltage f(t) and the system output voltage, y(t),
The problem asks that I derive a differential equation f(t) =... in terms of these functions and LL, RL, CL, CS.

So far, I've used KCL, where I = I(CL)+I(CS)...(1), which can be rewritten as dy(t)/dt * CL + dy(t)/dt * CS...(2).
After this I am unsure. I tried to find I initially with corresponding current equations for the resistor and inductor, but I got stuck.

Then I used KVL around the loop on the left, which gave f(t) = LL(dI/dt) + I(RL) + y(t).
Substituting equation 2 into I, I end up with:
f(t) = [LL(CL+CS) D^2 + RL(CL+CS)D + 1]y(t), where D is the operator for d/dt.

Is there something I'm missing? I am just pensive about my equation because the next question asks that I find the characteristic roots -- with LL=0.02, RL=0.50, CL=5.0, and CS=0.10, which end up being not-nice numbers for finding roots.

 

ugh... values without units

 

Is'nt implied ohms, farads, henrys ?

Regards, Dana.

 

Is'nt implied ohms, farads, henrys ?

In my experience, "implied" doesn't work very well in engineering.

 

Implied .... Think of the Mars mission in 1999 that missed the planet ... Implied

 

In my experience, "implied" doesn't work very well in engineering.

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Calling the variable voltage source voltage f(t) and the system output voltage, y(t),
The problem asks that I derive a differential equation f(t) =... in terms of these functions and LL, RL, CL, CS.

So far, I've used KCL, where I = I(CL)+I(CS)...(1), which can be rewritten as dy(t)/dt * CL + dy(t)/dt * CS...(2).
After this I am unsure. I tried to find I initially with corresponding current equations for the resistor and inductor, but I got stuck.

Then I used KVL around the loop on the left, which gave f(t) = LL(dI/dt) + I(RL) + y(t).
Substituting equation 2 into I, I end up with:
f(t) = [LL(CL+CS) D^2 + RL(CL+CS)D + 1]y(t), where D is the operator for d/dt.

Is there something I'm missing? I am just pensive about my equation because the next question asks that I find the characteristic roots -- with LL=0.02, RL=0.50, CL=5.0, and CS=0.10, which end up being not-nice numbers for finding roots.

Hello,

To start, why dont you just lump CL and CS into one single capacitor C and then go from there. That makes it a little simpler at least. Try that see what you get then.

I get a different result:
f(t)=D*C*R+DD*C*L+y

where D is first derivative dy/dt, DD is second derivative dy^2/d^2t,
C is the lumped C, R is your RL, L is your LL.

I did not check this too well yet but it looks right, so go over your equations again and see if you can match it.