# Find the natural response given the step response

Discussion in 'Homework Help' started by tquiva, Apr 4, 2011.

1. ### tquiva Thread Starter Member

Oct 19, 2010
176
1
Given the following step response of a circuit:

step(t)= 0, t<-2
= (t+2)^2, -2<t<0
= 4, t>0

(a) Carefully sketch and label the natural response of this circuit.

I know that step(t) + nat(t) = H(s)
w/ nat(t) being a special case of the step response (w/ a final value of zero)

I would have determined nat(t) = H(s) - step(t)

However, the transfer function wasn't given.
Is there a way to determine it given just the step response? Or is there another possible way to solve this problem?

Any help is appreciated. My thanks in advance.

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
Perhaps you might clarify the problem.

Presumably the response is what you have denoted as "step(t)".

What is the input step definition, if that is indeed the response?

Problems in the Laplace domain are normally defined for t>=0, with initial conditions satisfied at t=0, whereas your problem is not.

3. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
I'm guessing also that your reference to the natural response would normally be described by the inverse Laplace transform of the transfer function [H(s)], which is is also the time domain unit impulse response.

4. ### tquiva Thread Starter Member

Oct 19, 2010
176
1
For the unit step input: u(t) = 1 t>=0
= 0 t<0

So with ilaplace:

step(t) + nat(t) = H(t)

with the given information of the input unit step and step response, how can I find H(s) ?