Question

A single degree of freedom system has a mass of 2 kg, stiffness 8 N/m and viscous damping ratio 0.02. The dynamic magnification factor at an excitation frequency of 1.5 rad/s is

Answer 1

$MF=\frac{1}{\sqrt{{[1-{\left(\frac{\omega }{{\omega }_n}\right)}^2]}^2+{\left[2\zeta \frac{\omega }{{\omega }_n}\right]}^2}}$
Given, $\omega =$1.5 rad/s
${\omega }_n=\sqrt{\frac{k}{m}}=\sqrt{\frac{8}{2}}$=2 rad/s
$\zeta =0.02,\frac{\omega }{{\omega }_n}=\frac{1.5}{2}=0.75$
$\therefore MF=\frac{1}{\sqrt{[1-(0.75{)}^2{]}^2+(2\times 0.02\times 0.75{)}^2}}$
$\therefore MF=\frac{1}{\sqrt{(0.4375{)}^2+(0.03{)}^2}}=\frac{1}{\sqrt{0.1923}}$
$\therefore MF=2.28$