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Simple Harmonic Motion in Physics

Simple harmonic motion is what happens whenever the force pulling a body home grows in proportion to how far it has strayed. Springs do it, pendulums do it for small swings, and so does the vibration of a bridge or a molecule. The signature is that the acceleration always points back towards the centre and is proportional to the displacement, which makes the motion repeat with a period that never depends on how far the body swings. The blocks give that force and the timing it produces, the displacement, speed and acceleration at any instant, the energy that sloshes between kinetic and potential twice each cycle, and what happens once damping and driving are added.

Force exerted by a spring

Given

  • (N/m)
  • (m)
Angular frequency of a spring oscillator

Given

  • (N/m)
  • (kg)
Period of a spring oscillator

Given

  • (kg)
  • (N/m)
Frequency from the period

Given

  • (s)
Angular frequency from the frequency and the period

Given

  • (Hz)
  • (s)
Displacement in simple harmonic motion

Given

  • (m)
  • (rad/s)
  • (rad)
  • (s)
Acceleration in simple harmonic motion

Given

  • (rad/s)
  • (m)
Greatest speed in simple harmonic motion

Given

  • (m)
  • (rad/s)
Greatest acceleration in simple harmonic motion

Given

  • (m)
  • (rad/s)
Speed at a given displacement

Given

  • (m)
  • (rad/s)
  • (m)
Kinetic energy of a simple harmonic oscillator

Given

  • (N/m)
  • (m)
  • (m)
Potential energy of a simple harmonic oscillator

Given

  • (N/m)
  • (m)
Total energy of a simple harmonic oscillator

Given

  • (N/m)
  • (m)
Period of a simple pendulum

Given

  • (m)

Constant used

Period of a physical pendulum

Given

  • (kg m²)
  • (kg)
  • (m)

Constant used

Period of a torsional pendulum

Given

  • (kg m²)
  • (N m/rad)
Displacement of a damped oscillator

Given

  • (m)
  • (kg/s)
  • (kg)
  • (s)

Constant used

Angular frequency of a damped oscillator

Given

  • (N/m)
  • (kg/s)
  • (kg)
Amplitude of a driven oscillator at a given driving frequency

Given

  • (N)
  • (kg)
  • (rad/s)
  • (rad/s)
  • (kg/s)
Driving frequency at which resonance occurs

Given

  • (rad/s)