Question

What is the unit of damping factor?

Answer 1

Hint: To solve this question, we need to know the formula and definition of damping factor. Critical damping is defined as the approach of the moving system returning to its original position without undergoing oscillations.

Complete step-by-step solution:
Damping is an influence on a system that causes reduction, restriction, or prevention in its oscillation. Damping dissipates the energy stored in the oscillation. The damping ratio is a system parameter that describes how rapidly oscillations decay from one bound to another. Depending on its values, there are three types of damping. If the damping factor is zero, then the system is un-damped. If the damping factor is one, then the system is critically damped and if the damping factor is greater than one, then the system is overdamped. When the damping factor is less than zero, then the system is under-damped.
The damping factor is directly proportional to the spring stiffness or force constant ($k$) and inversely proportional to the mass of the object. The formula of damping factor is,
$C=2m\sqrt{\dfrac{k}{m}}$
The dimension of factor is $\left[ M \right]{{\left[ L \right]}^{2}}{{\left[ T \right]}^{-3}}$
Therefore, the SI unit of damping factor is $Ns/m$ .

Note:The damping factor can also be calculated using a direct and simplified equation which is $C=2\sqrt{km}$ .
Where, C is the damping factor, k is force constant and m is mass factor.
Also, between overdamped and underdamped cases, there is a certain level of damping at which the system will just fail to make a single oscillation. It is called critical damping.