Question: Using the Laplace transform, solve [ ddot{y}+2 dot{y}+y=F(t) ] where [ F(t)=u(t-1)-2 u(t-2)+u(t-3) ] is in terms of unit step functions, and (y(0)=0) and (dot{y}(0)=0).
Using the Laplace transform, solve
\[ \ddot{y}+2 \dot{y}+y=F(t) \]
where
\[ F(t)=u(t-1)-2 u(t-2)+u(t-3) \]
is in terms of unit step functions, and \(y(0)=0\) and \(\dot{y}(0)=0\).
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