Physics

Damping Ratio Calculator

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

Damping coefficient (N·s/m)

Spring constant (N/m)

Mass

Calculated Output

Damping ratio ζ 0.3162

Formula: ζ = c ÷ (2·√(k·m))

Step-by-Step Breakdown

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

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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.