Using Differential Equations to Solve a Series RLC Circuit

we don't do homework here

My apologies. Am in the wrong forum? Can this be moved?

Our rule on homework is stated in our FAQ. However, you've clearly done most of the work and has just reached a technical equivalent to a writer's block I'll give you a hint: If you know the current through a resistor, then what do you know about the voltage across the resistor.

that was a pretty big hint!!

Excuse me for my misunderstanding and I appreciate the help but the answer is Vr=2.31Sin2/3*e^-2t which I can't figure out by doing ohms law... Can someone explain this to me?

Yes, your professor can explain it.

If you taught our ee class we would probably learn much better. I actually went on my own course to do this using differential eqts. so I can see what is happening. In class we were given the Laplace formulas to "short cut" the problem, yet it doesn't help us learn the process of how we got there... Anyway, it finally occurred to me today morning that all I had to do was use the I=cdvdt formula to find the current since I already found v across capacitor. Your comment was very helpful, thanks for the answers and I,m glad there are some cr4 members that still try to help others.

I'm glad that TrevorM was able to give you the insight so you could solve your homework problem. Far to often people on the web (and even CR4) will just hand a student the answer. This usually leads to a completed assignment but no comprehension of the lesson. You'll find as circuit topology gets more complicated that the LaPlace transform will greatly expedite circuit and control system design. Particularly in the realms of filter and antenna design.

For Laplace transform, do you mean the phasors technique? I don't have a problem with that but one of the formulas defined by Laplace basically gives us the equation based on the over damped, under damped, critically damped analysis method for rlc circuits. It's great to have and a good way to check your answer IMO but i dont prefer it over kvl since it shows me what I,m doing. Also, for the problems you're referring to, are these 2nd order differential eqts or something more complex?

The phasor technique I think you're referring to is only valid with a first or second order Laplace differential equation. You will find in your education that Laplace is also excellent in black box analysis where an impulse or step input is applied to the box and the resultant output waveform informs the lumped response one must work with. This gets quickly into complex control theory that is many classes in your future.

Filter and control theory gets quickly into many orders of magnitude differential equations. Practical circuit implementations use multiple first and second order circuits cascading in series. A band pass filter with 18 db per octave slopes will be a sixth order differential equation. If one must have this band pass to be a delay equalized filter then even more differential equations must be included due to the all pass delay equalizing filter network.

I find that depending on the real world problem I confront, it will sometimes will be easier to approach the problem directly with differential equations or the LaPlace transform of a differential equation. Then again sometimes the implimentation must be digital instead of analog so a Z transform will be more suited.