An object with mass m = 2 is attached to a spring with spring constant k = 15 and immersed an environment that has a damping coefficient c = 2. the object is released from rest 2 units in the positive direction from the equilibrium position. between time t = 3 and time t = 5 the object is subjected to external forcing according to f(t) = 5 sin(2t). at time t = 8 an impulsive force with total impulse 8 is applied to the object. (a) give the ivp that will be solved by the displacement of the object from equilibrium position.
(b) solve the above ivp.