Enter the stiffness, mass, and damping coefficient to calculate the damping ratio.

Damping Ratio Calculation Formula

The following formula is used to calculate the damping ratio.

ζ = c / (2 * √(km))

Variables:

  • ζ is the damping ratio (dimensionless)
  • c is the damping coefficient (Ns/m)
  • k is the stiffness (N/m)
  • m is the mass (kg)

To calculate the damping ratio, divide the damping coefficient by twice the square root of the product of stiffness and mass.

What is Damping Ratio?

The damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance. In engineering, it is a crucial parameter that determines whether a system is underdamped, critically damped, or overdamped.

How to Calculate Damping Ratio?

The following steps outline how to calculate the damping ratio using the given formula.

  1. First, determine the stiffness (k), mass (m), and damping coefficient (c).
  2. Next, plug these values into the formula ζ = c / (2 * √(km)).
  3. Calculate the square root of the product of stiffness and mass.
  4. Multiply the result by 2.
  5. Divide the damping coefficient by the result from step 4 to find the damping ratio.
  6. Check your calculations using the calculator above.

Example Problem:

Use the following variables as an