Linear Vibrations Lab

An interactive companion for the vibrations unit of undergraduate dynamics. Read a little, then play with the simulations: every slider changes a real model, and every plot is computed live from the equations you are learning.

Every parameter has a slider and a box. Type any number into the box (press Enter or click away) to go beyond the slider range, or to try unusual values such as zero, negative damping or negative stiffness. The page explains what happens physically.

Contents

Equations of motion

Free-body diagrams, standard form, ωₙ and ζ, and when linearization works (pendulum demo).

Free undamped vibration

Initial conditions, amplitude and phase, phase portraits, and energy exchange.

Damped free vibration

Under-, critically and overdamped motion, and measuring ζ with the log decrement.

Forced harmonic vibration

Transient vs. steady state, resonance, beats, magnification and phase.

Base excitation

Moving supports, transmissibility and vibration isolation.

Summary & concept checks

A formula sheet and 21 questions with hidden answers.

Worked examples

8 problems with animations of each system and step-by-step solutions.

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How to use this site

Each chapter has a short explanation followed by live simulations. Drag a slider, or type any value into the box beside it, including values beyond the slider range, zero, or negative numbers. The page explains what happens physically when you try something unusual.

Every simulation has Pause, Restart, Default values and a speed menu.