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 ($f_n$), 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

Answer 1

The correct option is A 0.471 and 1.19 Hz

Stiffness of spring :
$k=3.6kN/m$

Damping constant of the damper

$C=400Ns/m$

$\text{Mass,}m=50kg$

$m\ddot{x}+c\dot{x}+kx=0$

[Suspension system consisting of spring and damper]

Damping factor,

$\left(d\right)or\xi =\frac{C}{C_c}=\frac{C}{2\sqrt{km}}$

$=\frac{400Ns/m}{2\sqrt{3.6\times {10}^3\times 50N/m\times kg}}$

${\omega }_n=\sqrt{\frac{k}{m}}=\sqrt{\frac{3.6\times {10}^3}{50}}$

Damped natural frequency,

${\omega }_d={\omega }_n\sqrt{1-{\xi }^2}=8.8485\sqrt{1-(0.471{)}^2}$

$2\pi f_d={\omega }_d=7.48\text{rad/s}$

$f_d=1.19\text{Hz}$