1) The suspension shock absorber acts to damp the body (sprung mass) resonance on the suspension spring. It also serves to control the wheel-hop (unsprung mass) resonance in which both the suspension spring and the tire spring are active. At sprung mass resonance, it is reasonable to assume that the axle is stationary with the sprung mass simply bouncing on the suspension. At wheel hop frequency, the sprung mass barely moves, so it is a reasonable approximation to model the axle as constrained between the ground and a stationary mass above the suspension. What is the damping ratio for the sprung and unsprung mass resonances of a quarter- car model with the following parameters? Ws = 1000 lb Ks = 100 lb/in Cs 11 lb-sec/in = Wu Kt = 1000 lb/in = = 100 lb 2) The undamped body bounce natural frequency of a quarter car model is often estimated several ways. In this problem, find out how much the estimates differ by computing the resonant frequency for a model with M = 1000 lb, m = 100 lb, K s = 100 lb/in, Kt 1000 lb/in. = a) For the sprung mass on the suspension stiffness (neglecting tire deflection) b) For the sprung mass on the suspension/tire combination, using the Ride Rate of the combination. c) For the total mass (sprung and unsprung) on the Ride Rate. d) Based on the quarter-car transmissibility equations (eqn. 5-14). Hint: In part d above, the damping is zero (Cs = 0), which greatly simplifies eqn. 5- 14. Resonance corresponds to the frequency, a, at which the denominator goes to zero (i.e., the gain of an undamped system goes to infinity). Although it first appears that the solution involves four frequencies, only two are real and they turn out to be the sprung mass resonance and the unsprung mass resonance. You simply want to find the sprung mass resonance frequency (the lowest one).