⚙️ EngineeringSimulation

Damped Oscillator

Plot the unit-step response of a second-order spring-mass-damper system. Adjust damping ratio ζ and natural frequency ωₙ to explore underdamped, critically damped, and overdamped behaviour.

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Parameters

Damping Ratio ζ

Natural Frequency ωₙ (rad/s)

Key Concepts

• ζ < 1: underdamped — oscillates, overshoots steady state
• ζ = 1: critically damped — fastest response without overshoot
• ζ > 1: overdamped — no oscillation, slow approach to steady state
• Overshoot = e^(−πζ/√(1−ζ²)) × 100% (underdamped only)
• Settling time t_s ≈ 4/(ζωₙ) for 2% criterion
• Models spring-mass-dampers, RLC circuits, and control loops

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