Question

Consider an open loop 1-degree-of-freedom mass-spring damper system. The system has mass 4.2 kg, and spring stiffness of 85.9 N/m, and damping coefficient of 1.3 N.s/m. What is the non-dimensional damping ratio of the system? Use at least 4 significant digits after the decimal point.

Answer 1

Answer:

Damping ratio  $\zeta =0.0342$

Explanation:

Given that

m=4.2 kg,K=85.9 N/m,C=1.3 N.s/m

We need to find damping ratio

We know that critical damping co-efficient

 $C_c=2\sqrt {mk}$

 $C_c=2\sqrt {4.2\times 85.9}$

 $C_c=37.98$ N.s/m

Damping ratio($\zeta$) is the ratio of damping co-efficient to the critical damping co-efficient

So $\zeta =\dfrac{C}{C_c}$

$\zeta =\dfrac{1.3}{37.98}$

$\zeta =0.0342$

So damping ratio  $\zeta =0.0342$