Vibration & Dynamics
Damped Frequency Simulator
Analyze a single-degree-of-freedom spring-mass-damper system. Modify mass, stiffness, and viscous damping to view real-time system responses.
State
Underdamped
ζ = 0.100
Crit. Damping
200.0
Ns/m
Output
CSV
Export ready
Parameters
Damping Preset
Vibration playback
System Governing Equations
Natural Frequency
ωn = √(k/m)
Critical Damping
Cc = 2√(k*m)
Damping Ratio
ζ = c/Cc
Damped Frequency
ωd = ωn√(1 - ζ²)
Current damping ratio ζ = 0.100 indicates an underdamped response.
The system oscillates with decaying amplitude.
Dynamic Visualizer
Damped Freq (ωd)
9.950rad/s
Natural Freq (ωn)
10.000rad/s
Damping Ratio (ζ)
0.100
Damped Freq (fd)
1.584Hz
Free Vibration Response
Response Coordinates
| Time t (s) | Displacement (m) |
|---|---|
| 0.000 | 1.0000 |
| 0.175 | -0.1457 |
| 0.351 | -0.6616 |
| 0.526 | 0.2954 |
| 0.702 | 0.3798 |
| 0.877 | -0.3187 |
| 1.052 | -0.1745 |
| 1.228 | 0.2752 |
| 1.403 | 0.0427 |
| 1.579 | -0.2062 |
| 1.754 | 0.0301 |
| 1.930 | 0.1365 |
| 2.105 | -0.0609 |
| 2.280 | -0.0783 |
| 2.456 | 0.0657 |
| 2.631 | 0.0360 |
| 2.807 | -0.0568 |
| 2.982 | -0.0088 |
| 3.157 | 0.0425 |