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

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{0, t>pi/2

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