So one of my homework problems for my introductory circuits class is to find the forced response for the voltage across a capacitor in an RLC circuit. The homework is online, and the system asks for the values of certain coefficients throughout the process of finding the forced response. I have been able to get all but one, the coefficient of the exponential function which represents the forced response. This is "b0" in my work attached. I am unsure where I am going wrong since I know "a1", "a0", and "p" seen in my work are correct.

 

First we need the problem statement. I see no initial conditions or switching information.

 

Here is the problem statement.

 

Here is the problem statement.

No, that is your solution. What was the question asked and is that the schematic that was in the problem statement or is that your simplification? Were you asked for the complete response or were you only asked for the forced response? Have you learned how to solve these with Laplace transforms or are you expected to solve this in the time domain?

 

So sorry, meant to attach this to the last post. The part I am stuck on is asking for the coefficient of the forced response which is an exponential function. I have not learned how to solve these with Laplace transforms.

 

So sorry, meant to attach this to the last post. The part I am stuck on is asking for the coefficient of the forced response which is an exponential function. I have not learned how to solve these with Laplace transforms.

Determine the boundary conditions for the diffeq. You need to evaluate the value of each term in the differential equation at t=0. To do that first you need to deduce the following.....

Vc(0) =
I(0) =
VL(0) =
dVc(0)/dt =
d^2 Vc(0)/dt =

e^xt for t=0 is conveniently equal to 1.
Then you just substitute back in to determine b0

 

Give up?

The voltage across the capacitor can not change instantly, nor can the current through the inductor (both = 0 at t=0). Using this information and the relationship of the (rate of change) derivatives of the voltage and currents in the cap and inductor respectively you can deduce the initial conditions you need to derive the coefficient.

Vc(0) = 0
I(0)= 0
VL(0) = 7
dVc(0)/dt = I(0)/C
d^2Vc(0)/dt = 1/C * dI(0)/dt = VL/LC
b0= VL/LC = 17.5

How does that work Cody?