The following is a two-mass model of a vehicle suspension.
m11 + c11 + k1x1 - c12 - k1x2 = 0
m22 + c12 + (k1 + k2)x2 - c11 - k1x1 = k2y
Mass m1 is one-fourth the mass of the car body, and m2 is the mass of the wheel-tire-axle assembly. Spring constant k1 represents the suspension's elasticity, and k2 represents the tire's elasticity. The input is the road surface displacement y. A certain vehicle has the following parameter values:
m1 = 250 kg
k1 = 1.5 x 104 N/m
m2 = 40 kg
k2 = 1.5 x 105 N/m
c1 = 1000 N.m/s
c2 = 0
(a) Obtain the suspension's frequency response plots. Determine the bandwidth and resonant frequencies, if any. (b) If the road surface is approximately sinusoidal with a period of 10 m, at what speeds will the car mass experience the greatest oscillation amplitude?