Question

A batting cage is designed by gluing a baseball to a spring-mass-dashpot system so that the ball is returned to the batter. The weight has mass 0.5kg which is attached to a spring which is stretched 2 meters by a force of 8 Newtons. Suppose the ball starts at equilibrium and a baseball player hits the ball, launching it at 20 meters per second. How strong should the dashpot be (in Newtons per meter/second i.e. the value of ”c” in class) so that when the ball returns to the hitter, it is traveling at a speed of 2 meters per second. [Hint: overdamping would prohibit the ball from ever returning to the hitter.]