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Second-Order Damping Ratio Calculator — result sheet
Calculate natural frequency and damping ratio from mass, damping coefficient, and spring stiffness.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Natural angular frequency=√(k/m); damping ratio ζ=c/(2√(km)).
The calculator reports the standard linear mass-spring-damper parameters from supplied coefficients.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Mass — minimum 1.0E-6; maximum 1000000
- Damping coefficient c — minimum 0; maximum 1000000
- Spring constant k — minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Mass | 2 |
| Damping coefficient c | 4 |
| Spring constant k | 50 |
Natural angular frequency =5 rad/s; damping ratio ≈0.2.
Assumptions and limits
- Mass and stiffness are positive and coefficients use compatible units.
- The system is linear with one degree of freedom.
- Nonlinear friction, forcing, geometry, and controller dynamics are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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