# Second order circuit - zero imput response

#### omar-rodriguez

Joined Jun 24, 2015
67
Hello, I have spent a lot of time trying to understand why I can't do this exercise by two different ways and find the same result.

I have to find Vc1(t) t ≥ 0 by two ways

1. first find the differential equation and then apply laplace transformation
2. second analyzing the circuit directly in the frequency domain

Solution:
1. find the differential equation and then apply laplace transformation

2. analyzing the circuit directly in the frequency domain

as you can see both answers are different and this this makes no sense..... I really don't know why HELP!!!

#### anhnha

Joined Apr 19, 2012
905
First, for the integral, you should take limits into account. By the way, why don't you Laplace and solve for I(s) in method 1?

#### omar-rodriguez

Joined Jun 24, 2015
67
I put the initial conditions after transform the differential equation

#### anhnha

Joined Apr 19, 2012
905
I put the initial conditions after transform the differential equation
Here is my result when solve for V1(t):