The spring pulls back.
Stiffness determines how aggressively displacement is pulled toward equilibrium. More stiffness raises the natural frequency.
Fspring = −kx
Why does it
keep bouncing?
Because the motion is underdamped: a strong impulse stores energy in a spring-like system, while too little damping lets it overshoot again and again.
ANIME PRESET / RUNNINGUNDERDAMPED
Damping ratio0.120
Natural frequency0.596 Hz
Peak displacement2.011 u
Zero crossings9
Settling time8.00+ s
Energy at 2s16.5%
The mechanism
One shove.
Three competing terms.
The phrase “anime physics” usually points to secondary motion that lags behind the main movement, overshoots its resting position, and takes conspicuously long to settle. A mass-spring-damper model isolates those ingredients.
The damper removes energy.
When damping is small, each swing loses only a little energy. That leaves room for several visible overshoots.
Fdamp = −cv
Mass resists
More mass makes acceleration slower for the same force and changes the rhythm of the response.
Impulse starts it
A sharp change in velocity supplies the initial energy. Stronger impulses increase amplitude, not the damping regime.
The ratio decides
ζ = c / 2√km. Below one, the system oscillates. At one, it returns fastest without overshoot.
What the eye reads
Bounce is a timing decision.
The anatomy is not the model. The model explains the motion signature: lag, overshoot, reversal, and decay.
Lag behind the driver
The primary body changes direction first. A flexible secondary mass continues on its old path, so the two movements separate in time.
LAGCross equilibrium
Stored spring energy carries the mass through rest. Low damping cannot remove that energy quickly enough, creating visible overshoot.
OVERDecay slowly
Every cycle is smaller, but a low damping ratio leaves several cycles large enough to notice. Animation can exaggerate this deliberately.
DECAYCompare responses
Same model.
Different feel.
Open each regime to connect the number to the visual result. The presets above use these same boundaries.
The exaggerated look comes from low damping, not from gravity changing.
Read the motion, not the label
Keep the evidence from your run.
The export records the inputs, equation, measured response, and the limits of this abstract model.