A projectile having a mass m = 10 kg is fired into a shock tube with a velocity V ₀ = 20 m/s

as shown in the figure. At the end of the tube the projectile impacts a stopper with a stiffness k = 40 kN/m and a damping coefficient e = 0.5 kN-sec/m. Determine (a) the maximum displacement of the projectile after impacting the stopper and (b) the time after impact at which the maximum displacement is attained. Plot the response of the system as a function of time. What is the ratio of the response if the system is undamped and the damped case [(xundampeid max / (Kdampea) max (10 pts) Shock tube Vo = 20 m/sec Rigid