(a) Consider a cart on a spring which is critically damped. At time t = 0, it is sitting at its equilibrium position and is kicked in the positive direction with velocityv_o.v o​ .Find its position x(t) for all subsequent times and sketch your answer. (b) Do the same for the case that it is released from rest at positionx = x_o.x=x o​ .In this latter case, how far is the cart from equilibrium after a time equal toτ_o = 2π/ω_oτ o​ =2π/ω o​ , the period in the absence of any damping?