Damped Oscillation Simulator

Simulate damped oscillations online — visualize overdamped, critically damped, and underdamped waveforms. Enter mass, spring constant, and damping coefficient

m x" + c x' + k x = 0

\u03C9\u2080 = \u221A(k/m), c_c = 2\u221A(km), \u03B6 = c/c_c

\u03B6 < 1: Underdamped | \u03B6 = 1: Critical | \u03B6 > 1: Overdamped

Input Parameters

Mass m (kg)

Spring constant k (N/m)

Damping coeff. c (Ns/m)

Initial disp. x₀ (m)

Results

Damping ratio \u03B6

0.100000

Classification

Underdamped

Natural freq. \u03C9\u2080

10.0000 rad/s

Critical damping c_c

20.0000 Ns/m

Damped freq. \u03C9_d

9.9499 rad/s

Damped period T_d

0.631484 s

Response x(t)