Question

In a spring-mass system with mass m = 0.5 kg and $K=200{Nm}^{-1}$, what is the value of damping coefficient for critical damping?

• A. 20 kg/sec
• B. 30 kg/sec
• C. 10 kg/sec
• D. 25 kg/sec

Answer 1

Answer: (A)

20 kg/sec

$m\frac{d^{2}x}{d{t}^2}+b\frac{dx}{dt}+kx=0---\left(1\right)$

Solution is of the form $x=e^{\lambda t}$

Putting $x=e^{\lambda t}$ in $\left(1\right)$

$m{\lambda }^2+b\lambda +k=0$

$\lambda =\frac{-c\pm \sqrt{c^2-4mk}}{2m}$

As critical dumping, $c^2-4mk=0$

Given $m=0.5kg$

$k=200N/m$

$C=\sqrt{4mk}=\sqrt{400}=20kg/s$

Damping coefficient $=20kg/s$