Please show all work for ffull rating An car suspension system has four parallel

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Please show all work for ffull rating

An car suspension system has four parallel springs each with stiffness k = 15 kN/m, four parallel shocks each with damping b, and has a mass of m = 1250 kg. The mass is centered between the two sets of wheels. Calculate the following: The natural frequency of the car fn in Hz. The value of b required for the damping ratio of the car to be zeta = 0.9. The damped natural frequency, fd, in Hz (omegad is in rad/sec) for the value of b found in part (b). The percent difference between fn and f. (100% middot(fn-fd)/fn).

Explanation / Answer

a) Equivalent k=4k, b=4b

fn=2*pi*sqrt(4k/m)=2*pi*sqrt(4*15/1250)=1.37 Hz

b)damping ratio=(4b)/2/sqrt(*4k*m)

=> b=0.9*2*sqrt(4*15*150)/4=42.69

c) fd=fn*sqrt(1-0.9^2)=1.37*sqrt(1-0.9^2)=0.59 Hz

d)percent diff.=fn-fd/fn=(1.37-0.59)/1.37*100=56.93%

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