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Consider the initial value problem $y_{??}+16y=g(t),y(0)=0,y_{?}(0)=0,$ where $g(t)={t0?if0?t<2if2?t<??$ a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of $y(t)$ by $Y(s)$. Do not move any terms from one side of the equation to the other (until you get to part (b) below). $=$ help (formulas) b. Solve your equation for $Y(s)$. $Y(s)=L{y(t)}=$ c. Take the inverse Laplace transform of both sides of the previous equation to solve for $y(t)$. If necessary, use $h(t)$ to denote the Heaviside function $h(t)={01?ift<0if0?t?$. $y(t)=$