Meaning and mechanism
When mass is connected to a spring, a restoring force proportional to the displacement acts. In a viscous damping model, a force proportional to the velocity, but in the opposite direction, acts.
If the damping is small, the amplitude decreases, and it returns without vibration when it is sufficiently large. The critical damping is the boundary that divides these two behaviors.
Relationships and conditions
mẍ+cẋ+kx=0 is the equation, and the critical damping coefficient is cc=2√(km). We compare c/cc to differentiate between under-damping, critical damping, and over-damping.
This is the free response of a linear spring and a constant viscous damping. Actual friction and large deformation may require different force laws, and the return time depends on the initial conditions and the reference.
What to observe in the simulation
Critical damping is the boundary for a fast nonoscillating return.
Analytic free vibration uses a linear spring and viscous damping. Release from rest at an initial road-shock displacement. Friction, nonlinear dampers and tires are omitted.
Key relationships and symbols
mẍ + cẋ + kx = 0 · cc = 2√(km)
| Symbol | Meaning | Unit |
|---|---|---|
| k | Spring stiffness | N/m |
| c | Viscous damping coefficient | N·s/m |
| m | Oscillating mass | kg |
Worked example
What is the critical damping coefficient?
2√(km) · Critical damping is the boundary for a fast nonoscillating return.
Common misconceptions
- If the damping is increased more dramatically, it is not always the case that it will reach equilibrium faster than the critical damping.