Car Suspension Bounce
Push down on the corner of a car and let go: does it settle at once or bounce like a boat? The spring sets how fast it bounces, the shock absorber how quickly it calms down.
Comfort or Control
A car body on its springs is a classic mass–spring–damper. Its natural frequency should be close to the pace of walking, around 1–1.5 bounces a second: softer feels floaty and leads to motion sickness, stiffer feels harsh. Sports cars go stiffer for better control.
The shock absorber turns motion into heat. Its strength is expressed as the damping ratio ζ: 0 bounces forever, 1 just stops without overshoot. Road cars use about 0.2–0.4; a worn damper drops far below that, and the car keeps bouncing after every bump.
Bounce After Letting Go
dampedKey Relations
How often the body would bounce without damping.
The damping relative to the critical value that just stops the bounce.
Released from rest at x₀; ωd = ωn√(1−ζ²). The overshoot is e^(−πζ/√(1−ζ²)).
Sources & Verification
- S. S. Rao, Mechanical Vibrations, 6th ed., Pearson, 2017 — Ch. 2 (Free Vibration of Single-Degree-of-Freedom Systems).
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 15 (Oscillations).