Physics

Damped Oscillator Calculator

Solve damped spring-mass response and classify damping regime.

Damped Oscillator Calculator analyzes spring-mass motion with damping to estimate displacement behavior over time. It is useful for dynamics study and control intuition. The tool helps identify underdamped, critically damped, or overdamped regimes. Use it to compare how damping changes response.

Damped Oscillator Inputs

Model: m x'' + c x' + k x = 0

Result

Natural frequency wn: 5.16397779 rad/s

Damping ratio zeta: 0.16137431

Regime: Underdamped

x(t): -0.0125867501 m

Damped period: 1.23289279 s

Approx settling time (5%%): 3.600000 s

How to use this tool

Enter mass, spring constant, damping coefficient, and initial conditions.
Run the solver to compute response parameters.
Inspect damping regime and compare behavior with altered coefficients.

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