Damped Oscillation

Under-, critically-, and over-damped motion

m·x'' + c·x' + k·x = 0 | ζ = c / (2√(mk))

Damping regime

Under-damped

Oscillates while the amplitude decays exponentially.

Natural frequency ω₀ (rad/s)

Damping ratio ζ

0.1

Natural period T₀ (s)

0.6283

Decay constant β (1/s)

Critical damping c_c (N·s/m)

Damped frequency ω_d (rad/s)

9.9499

Damped period T_d (s)

0.6315

Initial amplitude A (m)

1.005

Phase φ (rad)

0.1002

Decay time constant τ (s)

Quality factor Q

Logarithmic decrement δ

0.6315