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differential-equations

Damped free vibration: overdamped, critically damped, underdamped

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Local knowledge map

Amplitude response and resonance Beats Critically damped motion: the fastest non-oscillating return Energy in a vibrating mass-spring system Overdamped motion: two real decaying exponentials Steady-state versus transient response The damping ratio The mechanical-electrical analogy Damped free vibration: overdamped, critically damped, underdamped Cauchy-Euler with repeated and complex roots Complementary and particular solutions Complex Fourier series Long-term behavior and solution shape, read from the roots Oscillatory solutions, amplitude-phase form Repeated and complex roots at higher order The RLC circuit differential equation The eigenvalue method -- complex eigenvalues Undamped free vibration and natural frequency Complex roots and Euler's formula Distinct real roots Repeated real roots Setting up the mass-spring equation of motion Hooke's law and the spring restoring force The characteristic equation The general solution of a linear homogeneous equation

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