Damped Oscillator Calculator
Solve damped spring-mass response and classify damping regime.
Damped Oscillator Calculator analyzes spring-mass motion when damping removes energy from the system. Mass stores kinetic energy, the spring constant controls restoring force, and the damping coefficient represents friction, drag, or deliberate shock absorption. The undamped natural frequency describes how fast the system would oscillate without losses, while the damping ratio classifies behavior: underdamped systems oscillate while decaying, critically damped systems return quickly without overshoot, and overdamped systems return slowly without oscillation. Initial displacement and velocity set the starting state. This model is useful for vibration study, suspension intuition, and control-system checks, but real systems may include nonlinear springs, changing damping, external forcing, and structural limits.