Question

In a spring-mass system, the mass in m and the spring constant is k. The critical damping coefficient of the system is 0.1 kg/s. In another spring-mass syste, the mass is is 2 m and the spring constant is 8 k. The critical damping coefficient (in kg/s) of this system is

Answer 1

$\xi =\frac{C}{2\sqrt{mk}};C=2\xi \sqrt{mk}$
$\frac{C_2}{C_1}=\frac{2{\xi }_2\sqrt{m_2{k}_2}}{2{\xi }_1\sqrt{m_1{k}_1}}$
$\frac{C_2}{0.1}=\frac{2\times 1\sqrt{2m\times 8k}}{2\times 1\sqrt{m\times k}}$
$C_2=0.4$ kg/s

POINTS TO REMEMBER

If $\xi >1\Rightarrow$ Overdamped system $\Rightarrow$ No vibration
If $\xi =1\Rightarrow$ Critically damped system $\Rightarrow$ No vibration.
If $\xi <1\Rightarrow$ under damped system $\Rightarrow$ Vibration occur.