Question

A mass-spring-dashpot system with mass m =10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10 cos(25t)N. At the steady state, the vibration amplitude of the mass is 40 mm. The damping coefficiend (c, in Ns/m) of the dashpot is

Answer 1

Given, $m=10kg,F_0=10N$
$\omega =25$ rad/s $k=6250$ N/m
$X=\frac{F_0}{\sqrt{(k-m{\omega }^2{)}^2+(c\omega {)}^2}}$
or $\sqrt{(k-m{\omega }^2{)}^2+(c\omega {)}^2}=\frac{F_0}{X}$
$\left(c\omega \right)=\sqrt{{\left(\frac{F_0}{X}\right)}^2-(k-m{\omega }^2{)}^2}$

$=\sqrt{{\left(\frac{10}{0.04}\right)}^2-(6250-10\times 625{)}^2}$
$c\omega =\frac{10}{0.04}=250$
$\therefore c=\frac{250}{\omega }=\frac{250}{25}=10$ Ns/m