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)
10
Damping ratio ζ
0,1
Natural period T₀ (s)
0,6283
Decay constant β (1/s)
1
Critical damping c_c (N·s/m)
20
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)
1
Quality factor Q
5
Logarithmic decrement δ
0,6315