Damping Calculator

Calculate damping properties, analyze system response characteristics, and determine time domain metrics for mechanical and structural engineering applications.

Damping System Analysis
Calculate damping properties and behavior metrics

Calculate damping properties from mass, stiffness, and damping coefficient values.

A/A₀

Ratio of final to initial amplitude (0.1 = 10% of initial)

Calculation Results
Damping properties and system behavior

System Classification

—

Damping Properties

Damping Ratio (ζ)

—

Damping Coefficient

— N·s/m

Critical Damping

— N·s/m

Log Decrement (δ)

—

Frequency Response

Natural Frequency

— Hz

Damped Natural Freq.

—

Time Domain Metrics

Settling Time (2%)

— s

Rise Time

—

Peak Overshoot

0%

Time to 0.1 A₀

—

More Information
Understanding damping behavior in mechanical and structural systems

Damping Classifications

Underdamped (ζ < 1)

System oscillates with gradually decreasing amplitude. Most real-world systems are underdamped, such as vehicle suspensions and guitar strings.

Critically Damped (ζ = 1)

System returns to equilibrium in the minimum possible time without oscillation. Ideal for systems requiring fast response without overshoot.

Overdamped (ζ > 1)

System returns to equilibrium without oscillation, but more slowly than a critically damped system. Examples include door closers.

Key Equations

Damping Ratio

ζ = c / (2√(km))

Where c is damping coefficient, k is stiffness, m is mass

Logarithmic Decrement

δ = ln(x₁/x₂) = 2πζ/√(1-ζ²)

For underdamped systems, ratio of successive peak amplitudes

Settling Time

Ts = 4/(ζωn)

Time to reach and stay within 2% of final value

Engineering Applications

  • Vibration Control: Isolating sensitive equipment from ground vibrations
  • Structural Dynamics: Designing structures to withstand earthquake forces
  • Vehicle Suspensions: Optimizing ride comfort and handling
  • Precision Instruments: Preventing oscillation in measuring devices
  • Shock Absorbers: Dissipating energy in impact scenarios
  • Control Systems: Achieving desired transient response characteristics

Experimental Determination

Damping properties can be determined experimentally by:

  1. Recording free vibration response of a system after an initial disturbance
  2. Measuring successive peak amplitudes x₁ and x₂
  3. Calculating logarithmic decrement δ = ln(x₁/x₂)
  4. Deriving damping ratio ζ = δ/√(4π²+δ²)

Related Calculator

For frequency domain analysis and resonance phenomena, check our Resonance Calculator, which provides insights into system frequency response and vibration characteristics.