# 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!

• ###### Sol.GIF
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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
783
Another approach might be using the Laplace Transform

$4s^2Y(s)=2X(s)-sX(s)$

or

$H(s)=\frac{Y(s)}{X(s)}=(-\frac{1}{4})\frac{(s-2)}{s^2}$

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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Jul 10, 2011
33
1

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
783
That's correct