What Is the SDOF Natural Frequency & Damping Ratio Calculator?
An SDOF system models an idealized dynamic structure whose configuration can be fully specified by a single displacement coordinate.
How Does the SDOF Natural Frequency & Damping Ratio Calculator Work?
Computes angular frequency ωn = √(k/m).
Computes critical damping coefficient cc = 2·√(k·m).
Calculates damping ratio ζ = c / cc.
Identifies vibration regime (underdamped, critically damped, or overdamped).
SDOF Natural Frequency & Damping Ratio Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
ωn = √(k / m), fn = ωn / (2π), cc = 2·√(k·m), ζ = c / cc, ωd = ωn·√(1 - ζ²)
Fundamental equations of motion for damped harmonic single degree of freedom oscillators.
How to Use the SDOF Natural Frequency & Damping Ratio Calculator
- Enter mass in kg and stiffness in N/m.
- Enter viscous damping coefficient in N·s/m.
Step-by-Step Example Calculation
Mechanical Equipment Isolation Mount
Input Values:
mass:100
stiffness:40000
dampingCoeff:200
Worked Steps: 100 kg machine on 40 kN/m spring mounts with 5% damping.
Understanding Your Result
Primary output reports natural frequency in Hz.
Summary displays natural period, damping ratio, and vibration regime.
Factors That Affect the Result
- Stiffness-to-mass ratio.
When Should You Use This Calculator?
- Vibration isolation, earthquake structural analysis, and machine balancing.
Assumptions & Limitations
- Assumes linear elastic stiffness and linear viscous dashpot damping.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact analytical solution of second-order linear ODE.