Hi I've an exam on system dynamics in a few weeks and as trying to understand whats going on.

Here is the problem I'm currently stuck on and it's wrecking my head.

With the assistance of laplace transform tables determine an expression for the response of the system.

T(s) = 1/(s^2+0.2s+1)

when subject to a unit ramp input. Assume initial conditions are zero.

Answer given:

y(t) = t-0.2-0.96((e^(-0.1t))/0.995)sin(0.995t)-0.2((e^(-0.1t))/0.995)sin(0.995t-1.471) , t > 0

I just can't find any book or web site that could explain me how to do this.

so far my working are:

1/(s^2+0.2s+1) = (1/0.995)(0.995/(s+0.1)^2+0.995^2)

which transforms into (1/0.995)((e^(-0.1t))/0.995)sin(0.995t)

But well this is not the answer ... I'm sure I'm supposed to do something about it been subject to a unit ramp input but this is where I'm getting completly lost.

Please can someone Help me??

Thanks

Bob.