Second order circuit - zero imput response

Discussion in 'Homework Help' started by omar-rodriguez, Mar 8, 2016.

  1. omar-rodriguez

    Thread Starter Member

    Jun 24, 2015
    51
    2
    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.

    [​IMG]

    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
    [​IMG]
    2. analyzing the circuit directly in the frequency domain
    [​IMG]
    [​IMG]
    as you can see both answers are different and this this makes no sense..... I really don't know why HELP!!!
     
  2. anhnha

    Active Member

    Apr 19, 2012
    774
    48
    Your first solution is wrong.
    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?
    upload_2016-3-9_9-2-6.png
     
  3. omar-rodriguez

    Thread Starter Member

    Jun 24, 2015
    51
    2
    I put the initial conditions after transform the differential equation
     
  4. anhnha

    Active Member

    Apr 19, 2012
    774
    48
    Here is my result when solve for V1(t):

    Solve for Voltage.PNG
     
    omar-rodriguez likes this.
  5. omar-rodriguez

    Thread Starter Member

    Jun 24, 2015
    51
    2
    Great!!, finally I undestood my mistake thank you
     
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