Question

A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m and the damping constant of the damper is 400 Ns/m. If the mass is 50 kg, then the damping factor (d ) and damped natural frequency (fn), respectively, are

(a) 0.471 and 1.19 Hz

(b) 0.471 and 7.48 Hz

(c) 0.666 and 1.35 Hz

(d) 0.666 and 8.50 Hz

This question was addressed to me in examination.

My query is from Bifilar and Trifilar Suspension topic in chapter Simple Harmonic Motion of Machine Kinematics

Answer 1

Right option is (a) 0.471 and 1.19 Hz

Explanation: Given k = 3.6 kN/m, c = 400 Ns/m, m = 50 kg

We know that, Natural Frequency

ωn = √k/m = 8.485 rad/ sec

And damping factor is given by,

d or ε = c/cc

       = 0.471

Damping Natural frequency,

ωd = √1 – ε^2ωn

2πfd = √1 – ε^2ωn

fd = 1.19 Hz.