# impulse response

#### hamza324

Joined Jul 10, 2011
33
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

#### tgotwalt1158

Joined Feb 28, 2011
110
I find a clue from my old differential equation recollection, might help you!

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• hamza324

#### hamza324

Joined Jul 10, 2011
33

#### t_n_k

Joined Mar 6, 2009
5,455
Another approach might be using the Laplace Transform

or

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.

• hamza324

#### hamza324

Joined Jul 10, 2011
33

#### hamza324

Joined Jul 10, 2011
33
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..??

#### t_n_k

Joined Mar 6, 2009
5,455