impulse response

Discussion in 'Homework Help' started by hamza324, Sep 21, 2011.

  1. hamza324

    Thread Starter Member

    Jul 10, 2011
    33
    1
    i want to know the impulse response to the following

    4y''(t) = 2x(t) - x'(t)

    I am able to solve this problem without the x'(t) on the right hand side but i am not sure how to deal with x'(t). The way i was told to this is to integrate it through "0 negative " to " 0 positive" thanks
     
  2. tgotwalt1158

    Member

    Feb 28, 2011
    111
    18
    I find a clue from my old differential equation recollection, might help you!
     
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  3. hamza324

    Thread Starter Member

    Jul 10, 2011
    33
    1
    thanks.this will help..
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Another approach might be using the Laplace Transform

    [​IMG]

    or

    [​IMG]

    For which the impulse response is the inverse transform of H(s), giving the output y(t) as ....[for t>=0]

    y(t)=\frac{t}{2}-\frac{1}{4}

    Which agrees with tgotwalt1158's solution.
     
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  5. hamza324

    Thread Starter Member

    Jul 10, 2011
    33
    1
    thanks for your help...this is helpful...
     
  6. hamza324

    Thread Starter Member

    Jul 10, 2011
    33
    1
    i solved another question for impulse response
    y'' + 9 y= -6x'

    after doing laplace i get

    Y = -6s/(s^2 + 9)


    and so y(t) =-6 cos3t .

    is it correct..??
     
  7. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    That's correct
     
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