Step Response of System with Pole in s = 0 at Infinity

[pivu0]

Homework Statement

A contininous time system has when laplace transformed, a pole in s = 0.
What is de stepresponse for the system when t goes to infinity

Homework Equations

H(s) is infinity in 0 (H(s) is unit response laplace transformed)
s(t) = h(t) * u(t) (the stepresponse is the output of a system when the input is the unit step function)(* means convolution)

The Attempt at a Solution

It's a MC
a) infinity
b) 0
c) finit

I thought the anwser is b, because when a input is put in s = infinity is would equal zero the input would only have a valeu if it is near t = 0

 

[n.karthick]

I thought the anwser is b, because when a input is put in s = infinity is would equal zero the input would only have a valeu if it is near t = 0

No, it is step input, so it will be present from t=0 onwards.
One thing to be noted is convolution in time is multiplication in frequency domain.
Hence the system response with step input will be 1/s^2. Taking inverse Laplace transform will give you the output as function of t.

 

[pivu0]

No, it is step input, so it will be present from t=0 onwards.
One thing to be noted is convolution in time is multiplication in frequency domain.
Hence the system response with step input will be 1/s^2. Taking inverse Laplace transform will give you the output as function of t.

I have made a mistake in OP, I ment that H(s) is the impulse reponse in s, not the unti response!
So, one can say that because there is only 1 pole in s = 0, the H(s) is 1/s ?
U(s) is also 1/s,
You say that convolution is multiplication in freq domein, do you mean S(s) = H(s)*U(s) ?
So that means the laplace transform of the step response is 1/s^2!

Thank you for your help!