Laplace transform problem

Discussion in 'Homework Help' started by xxxyyyba, Jul 11, 2013.

  1. xxxyyyba

    Thread Starter Member

    Aug 7, 2012
    249
    2
    My task is to solve circuit below using Laplace transform:
    [​IMG]
    Firstly, I solved it using complex numbers and I got:
    [​IMG]
    I'm sure it's correct. Here is my solution using Laplace transform:
    [​IMG]
    [​IMG]
    [​IMG]
    It's obvious that solutions I got using complex numbers and Laplace transform are different. Where did I make mistake?
     
  2. WBahn

    Moderator

    Mar 31, 2012
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    My first guess would be that you aren't using the same driving function in both cases. Hint: The transform you used is the single-sided Laplace transform.
     
  3. xxxyyyba

    Thread Starter Member

    Aug 7, 2012
    249
    2
    Should I use two-sided Laplace transform? Just to mention that I don't have any problem in RC circuit analysis using single-sided Laplace transform.
     
    Last edited: Jul 12, 2013
  4. WBahn

    Moderator

    Mar 31, 2012
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    But a single-sided transform means that the function being transfomed is taken to be identically zero for all time t<0. But the steady state analysis you did first assumes that the sinusoidal voltage is, always has been, and always will be sinusoidal.

    Do you expect a circuit that has been running in sinusoidal steady state to have the same response for t>0 as the same circuit that has a sinusoidal source suddenly turned on at t=0?
     
  5. xxxyyyba

    Thread Starter Member

    Aug 7, 2012
    249
    2
    Does it mean that my calculations include both transient and steady-state response?
     
  6. WBahn

    Moderator

    Mar 31, 2012
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    I would expect it to.

    But you answer has more than one problem. Notice that it is always positive. Does that make sense?
     
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