# Thread: Laplace Transforms - find the system response

1. ## Laplace Transforms - find the system response

Hello,

I'm stuck part way through this:

A Linear, time invariant system has the impulse response $\displaystyle h(t) = tu(t-1)$ Find the transfer function $\displaystyle H(s)$ and use it to find the response to the input $\displaystyle x(t) = u(t) - 2u(t-1) + u(t-2)$

I have found $\displaystyle H(s) = \frac{e^{-s}}{s^2} + \frac{e^{-s}}{s}$

And $\displaystyle X(s) = \frac{1}{s} - \frac{2e^{-s}}{s} + \frac{e^{-2s}}{s}$

But I'm confusing myself in the algebra to find Y(s)... I keep ending up with long, confusing equations. I can't seem to find the correct form for the inverse laplace transform...

I would prefer a few hints in the right direction or a starter rather than a full blown solution if you could

2. ## Re: Laplace Transforms - find the system response

Originally Posted by halfnormalled
Hello,

I'm stuck part way through this:

A Linear, time invariant system has the impulse response $\displaystyle h(t) = tu(t-1)$ Find the transfer function $\displaystyle H(s)$ and use it to find the response to the input $\displaystyle x(t) = u(t) - 2u(t-1) + u(t-2)$

I have found $\displaystyle H(s) = \frac{e^{-s}}{s^2} + \frac{e^{-s}}{s}$

And $\displaystyle X(s) = \frac{1}{s} - \frac{2e^{-s}}{s} + \frac{e^{-2s}}{s}$

But I'm confusing myself in the algebra to find Y(s)... I keep ending up with long, confusing equations. I can't seem to find the correct form for the inverse laplace transform...

I would prefer a few hints in the right direction or a starter rather than a full blown solution if you could
The impulse response is $\displaystyle h(t)=t\ u(t-1)$ and it has 'only one' term in t... then why the tranform of h(t) You computed has two terms in s?...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$