The following differential equation provides a simple model of a suspension system. The constant m gives the mass of moving parts, the constant k relates to stiffness of the suspension system and the constant c is a measure of the damping in the system. F is a constant force applied at t = 0

m? + c? + kx = F

Given that m = 1, k = 4, F = 1 and both x = 0 and dx/dt = 0 when t = 0, determine the responses, x(t) for t = 0 to 8 and plot x(t) for each case in one graph. Remember to label each curve.use mat lab

1. c=0

2. c=sqrt(mk)

3. c=2*sqrt(mk)

4. c=4*sqrt(mk)