Oscillations and Waves - Theory & Concepts - Harmonic Motion

Oscillations (vibrations) are back-and-forth motions about an equilibrium position. Waves are propagating disturbances that carry energy from one place to another without permanently moving the medium itself. Understanding these phenomena is critical for structural engineering (earthquake resistance, wind-induced vibrations) and acoustics.

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Interactive engineering simulation

Simple Harmonic Motion & Damping

Study the oscillatory behavior of a mass-spring system. Introduce damping to see how the system transitions from standard oscillation to critical and overdamping.

Mass (m)1.0 kg

0.5–5.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Spring Constant (k)10 N/m

N/m

2–50

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Initial Amplitude (x0)0.5 m

0.1–1.5

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Damping Coefficient (c)0.0 kg/s

kg/s

0.0–5.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Damping Ratio (ζ) & State

0.00Undamped

Governing Formulas

Motion Equation

m \ddot{x} + c \dot{x} + k x = 0

Natural Angular Freq

\omega_0 = \sqrt{k/m}, \quad \zeta = \frac{c}{2\sqrt{km}}

Natural Freq0.50 Hz

Period (T)1.99 s

Position (x)0.50 m

Velocity (v)0.00 m/s

Model scope and verification

Use the displayed units and idealizations, then verify the governing balance or compatibility equation before interpreting the result.

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