Mass-spring motion can be modeled by the ordinary differential equation m x^{\prime \prime}+c x^{\prime}+k x=f(t) where m is the mass, c is the damping coefficient, k is the spring stiffness

and f(t) is the external applied force. 1. Set m = 1, k = 25 and f(t) = 0 for this problem. The damping coefficient will be allowed to vary. The initial conditions are x(0) = 1 and x' (0) = 0. Solve the IVP for the following four cases c= 0,6,10, 12 using paper and pencil.