Damping Ratio Calculator

Find the damping ratio of a spring-mass-damper system.

Damping coefficient (N·s/m)

Spring constant (N/m)

Mass

Damping ratio ζ 0.3162

Formula: ζ = c ÷ (2·√(k·m))

Step-by-step with your numbers:

1. Values used:

2. Damping coefficient = 20 N·s/m

3. Spring constant = 500 N/m

4. Mass = 2

6. Damping ratio ζ = 0.3162

Did we solve your problem today?

The damping ratio describes how oscillations decay in a vibrating system.

The math behind it

ζ = c ÷ (2√(km)). ζ < 1 is underdamped (oscillates), ζ = 1 is critically damped, ζ > 1 is overdamped.

c = 20, k = 500, m = 2 → ζ ≈ 0.316 (underdamped).

What is critical damping?

ζ = 1, the fastest return to rest without overshooting.