1. An engineering model of a person bouncing on a diving board is shown below. The diving board is modeled as a rigid beam of length L that can pivot about one end. The mass of the board is lumped at the free end and a spring and damper at this end model the board stiffness and energy dissipation respectively. The diver is modeled simply as a lumped mass. Assume small rotation angles (although this assumption may not be adequate in a more thorough analysis).
• Find the differential equation governing the motion of the diver while she is in contact with the board. Neglect any rotational inertia. You cannot neglect the weight of the diver in this equation if we measure the displacement as shown, i.e. from the equilibrium posi-tion of the diving board without the weight of the diver.For the remainder of the problem assume the diver weighs 120 lbf, the effective weight of the board is 30 lbf, the length of the board is 6 ft, the spring constant is 300 lbf/ft, and the damp-ing coef?cient is 4 lbs-s/ft. The diver begins her initial descent towards the board a distance d = 3 ft above the board.
• Use conservation of energy and momentum to determine the diver's velocity when she contacts the board and the initial velocity of the system.
• What is the peak de?ection of the diving board?
2. Plot the force between the diver and the board as a function of time.
• Determine the time the diver loses contact with the board?
• Determine how high will she go above the board's equilibrium position, i.e. above y = 0?
(Assume she does not jump off the board, i.e. she does not add any energy to the system.)
3. Determine how much energy was dissipated in the damper and how much gravitation poten-tial energy the diver lost.
