Laplace Transform Example: Series RLC Circuit
Problem
Given a series RLC circuit with , , and , having power source , find an expression for if and .
Solution
We begin with the general formula for voltage drops around the circuit:
Substituting numbers, we get
Now, we take the Laplace Transform and get
Using the fact that , we get
Using partial fraction decomposition, we find that
Finally, we take the inverse Laplace transform to obtain
which is our answer.