Differential Equations math homework help

Consider the initial value problem

modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force
$F(t)$ , where the unit of force is the Newton (N). Assume that
$m = 2$ kilograms,
$c = 8$ kilograms per second,
$k = 80$ Newtons per meter, and the applied force in Newtons is

{20, 0<=t<=pi/2

{0, t>pi/2

For $t > pi/2″ style=””>, <img decoding=$

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