Examples for

Oscillations & Waves

Covering oscillatory motion from pendulums to electromagnetic waves, Wolfram|Alpha supports a wide range of formulas, equations and computations to cover the physics of oscillations and waves. Find the properties of mechanical waves, play sound waves and calculate the motion of spinning tops.

Simple Harmonic Motion

Explore the properties of a wide range of simple harmonic oscillators such as springs, pendulums and torsion systems.

Analyze a harmonic oscillator:

Find equations associated with a harmonic oscillator:

Motion of a Top

Explore the precession, nutation and evolution of motion for a spinning top.

Analyze the motion of a symmetric top:

Find the equations of motion:

Pendulum Motion

Calculate the harmonic motion for a large range of pendulum types including double, coupled and torsion pendulums.

Analyze the motion of a simple pendulum:

Analyze the motion of a spring pendulum:

Find the Lagrangian of a system:

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Sound & Acoustics

Compute the properties and perception of sound as well as how it interacts with matter.

Compute a Doppler shift:

Find the maximum distance for hearing a sound:

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Step-by-Step Solutions for Physics


  • Electromagnetic Radiation
  • Optics
  • Tides
  • Waveguides

    Compute the features of electromagnetic waves within waveguides and resonant cavities.

    Explore properties of ideal waveguides:

    Find mode frequencies and quality factors for resonant cavities:

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