Damped Oscillation Calculator

Analyze damped harmonic oscillators. Calculate position, velocity, and energy decay for underdamped, critically damped, and overdamped systems.

System Parameters

1 kg
0.1 kg100 kg
kg
100 N/m
1 N/m1,000 N/m
N/m
2 kg/s
0.1 kg/s50 kg/s
kg/s

Critical damping: 20.0000 kg/s

0.5 m
0.01 m2 m
m
1 s
0 s20 s
s

Damping Type

Underdamped

Damping ratio (ζ) = 0.1000

xPosition at t=1s
-0.159159 m
vVelocity at t=1s
1.076620 m/s
ω₀Natural Frequency
10.0000 rad/s
ωdDamped Frequency
9.9499 rad/s
TDamped Period
0.6315 s
QQuality Factor
5.0000

Energy Decay:

Initial Energy

12.500000 J

Current Energy

1.691691 J

τTime Constant
1.0000 s
δLogarithmic Decrement
0.6315

What is Damped Oscillation?

Damped oscillation occurs when a system experiences a resistive force (such as friction or air resistance) that dissipates energy over time. The amplitude of oscillation decreases exponentially. Depending on the damping strength, the system can be underdamped (oscillates with decreasing amplitude), critically damped (returns to equilibrium fastest without oscillating), or overdamped (returns slowly without oscillating).

Damping Types

Underdamped (ζ < 1)

System oscillates with exponentially decreasing amplitude

Critically Damped (ζ = 1)

Fastest return to equilibrium without oscillation

Overdamped (ζ > 1)

Slow return to equilibrium, no oscillation