Critical Damping Ratio Calculator

Enter the damping coefficient, mass, and stiffness into the calculator to determine the critical damping ratio.

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Critical Damping Ratio Formula

The following formula is used to calculate the critical damping ratio for a given damping coefficient, mass, and stiffness.

(zeta = \frac{c}{2 \sqrt{m \cdot k}})

Variables:

(zeta) is the critical damping ratio
(c) is the damping coefficient
(m) is the mass
(k) is the stiffness

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

What is Critical Damping Ratio?

The critical damping ratio is a dimensionless measure of damping in a system relative to critical damping. It indicates how oscillations in a system decay after a disturbance. A system is critically damped when the damping ratio is equal to 1, meaning it returns to equilibrium as quickly as possible without oscillating. If the damping ratio is less than 1, the system is underdamped and will oscillate. If the damping ratio is greater than 1, the system is overdamped and will return to equilibrium slowly without oscillating.

How to Calculate Critical Damping Ratio?

The following steps outline how to calculate the Critical Damping Ratio.

First, determine the damping coefficient ((c)).
Next, determine the mass ((m)).
Next, determine the stiffness ((k)).
Finally, calculate the critical damping ratio using the formula (zeta = frac{c}{2 sqrt{m cdot k}}).
After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Damping Coefficient ((c)) = 50 Ns/m

Mass ((m)) = 10 kg

Stiffness ((k)) = 200 N/m