Q$1.(10$ pts $).$ Consider the frictionless movement of a mass m shown in Figure $($a$),$ where $f(t)$ is the force applied, $y(t)$ is the displacement of the mass, and $m=1kg.$ Using the Laplace transform, find $y(t)$ for $t>0$ if $f(t)$ has the form shown in Figure $($b$)$ and the initial conditions are $y(0)=1$ dy$/$dt $(0)=0.$