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Math Help - [SOLVED] Particular Solution For Impulse

  1. #1
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    [SOLVED] Particular Solution For Impulse

    Hi everybody,

    For example a diff. eqn

    (D^3+D^2+D+1)h(t)=impulse(t)

    I learn that particular solution for impulse(t) is

    h(t)=Xh(t).u(t) where Xh(t) is homogenous soln. and u(t) is step fn.

    But I did not understand this derivation, how this expression is particular soln. for impulse?

    How can we determine coeff. appears in homogenous soln. and then our particular soln. become well known?

    Thanks a lot.
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  2. #2
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    Quote Originally Posted by alper View Post
    Hi everybody,

    For example a diff. eqn

    (D^3+D^2+D+1)h(t)=impulse(t)

    I learn that particular solution for impulse(t) is

    h(t)=Xh(t).u(t) where Xh(t) is homogenous soln. and u(t) is step fn.

    But I did not understand this derivation, how this expression is particular soln. for impulse?

    How can we determine coeff. appears in homogenous soln. and then our particular soln. become well known?

    Thanks a lot.
    Using the theory of Laplace transforms is one possible approach.
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  3. #3
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    Thanks a lot.

    After I posted my problem here, I found a signal book. It explains my question very well. I think I understood.

    By the way, using the Laplace Transformation, what should I assume initial conditions? Zero?
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