Damping Ratio Calculator

Formula

To calculate the Damping Ratio (\(\zeta\)):

\[ \zeta = \frac{c}{2 \sqrt{km}} \]

Where:

\(\zeta\) is the Damping Ratio
\(c\) is the damping coefficient (Ns/m)
\(k\) is the spring constant (N/m)
\(m\) is the mass (kg)

What is the Damping Ratio?

The Damping Ratio (\(\zeta\)) is a measure of how oscillations in a system decay after a disturbance. It is calculated by dividing the damping coefficient by twice the square root of the product of the mass and the spring constant. The damping ratio helps determine whether a system is underdamped, critically damped, or overdamped.

Example Calculation 1

Let's assume the following values:

Mass (\(m\)) = 50 kg
Spring Constant (\(k\)) = 500 N/m
Damping Coefficient (\(c\)) = 100 Ns/m

Using the formula:

\[ \zeta = \frac{100}{2 \sqrt{500 \times 50}} = 0.3162 \]

The Damping Ratio is 0.3162.

Example Calculation 2

Let's assume the following values:

Mass (\(m\)) = 30 kg
Spring Constant (\(k\)) = 300 N/m
Damping Coefficient (\(c\)) = 60 Ns/m

Using the formula:

\[ \zeta = \frac{60}{2 \sqrt{300 \times 30}} = 0.5477 \]

The Damping Ratio is 0.5477.