Problem 1: Energy absorbing car bumper has an equivalent spring constant of $525 \mathrm{kN} / \mathrm{m}$, and is initially undeformed. The $1200-\mathrm{kg}$ car approaches a massive wall with a speed of $8 \mathrm{~km} / \mathrm{h}$, and collides with it. Treat the collision of the car with the wall as a single-DOF system and determine the maximum deflection of the bumper and the speed with which the car rebounds back for the following two cases: a) No energy dissipation b) Bumper has a damping ratio of 0.1

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