(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the unit step response of the transfer function...

a) [tex]G(s)\,=\,\frac{4}{s\,+\,4}[/tex]

b) [tex]G(s)\,=\,\frac{2}{0.2s\,+\,1}[/tex]

2. Relevant equations

General first order step response equation...

[tex]C(s)\,=\,R(s)\,G(s)\,=\,\frac{a}{s(s\,+\,a)}[/tex], where [tex]R(s)\,=\,\frac{1}{s}[/tex]

then do an inverse Laplace transform...

[tex]c(t)\,=\,1\,-\,e^{-at}[/tex]

3. The attempt at a solution

Part a) is simple enough. I just plugged into formula above and got [tex]c(t)\,=\,1\,-\,e^{-4t}[/tex]

However, part b) is where I am confused. To get the G(s) into the form needed (i.e. ~ [itex]\frac{a}{s\,+\,a}[/itex]), I divided both the numerator and denominator by 0.2...

[tex]G(s)\,=\,\frac{2}{0.2s\,+\,1}\,=\,\frac{10}{s\,+\,5}\,=\,2\left(\frac{5}{s\,+\,5}\right)[/tex]

But now the form is not exactly as needed in the first order system equations. What do I do?

I tried taking out a 2 from the numerator, and got an answer, just not sure if it's right though.

Is this right for part b)...

[tex]c(t)\,=\,2\,\left[1\,-\,e^{-5t}\right][/tex]

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# Homework Help: Step response of a first order system

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