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- #1

\[

H(s) = \frac{Y(s)}{U(s)} = \frac{1}{s + 1}

\]

and

\[

u(t) = 1(t) + 1(t - 1).

\]

How do I find U(s)? I know I take the Laplace transform of u(t) but with the two step functions how can this be done?

The Laplace transform of the step function is \(\frac{1}{s}\) for \(t > a\) where \(a\) is the shift. If I take the Laplace of \(u(t)\), do just get

\[

\frac{2}{s}\mbox{?}

\]

That seems strange though since \(\frac{1}{s}\) is for \(t > 0\) and the other \(\frac{1}{s}\) is for \(t > 1\).

The end goal is to find \(y(t)\).