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The 35 pages that link to Simple harmonic motion, each with the reason it gives.

• RadianRelated: Its phase and angular frequency are conventionally expressed in radians.

• AmplitudeNarrower topic: Its equilibrium position and maximum displacement provide the basic model for defining amplitude.

• PendulumRelated: A pendulum approximates this motion when its swings are small.

• SineRelated: An ideal oscillator’s position can be written as a sine function of time.

• Periodic functionRelated: Its position and velocity are canonical periodic functions in mechanics.

• DampingNarrower topic: It is the undamped baseline against which decay and altered frequency are defined.

• Trigonometric functionsRelated: Sine and cosine describe ideal oscillations such as a mass on a spring.

• Angular frequencyBroader topic: Its sinusoidal motion advances phase at a constant angular frequency.

• Acoustic resonanceRelated: It provides a basic model for the oscillatory systems that can resonate acoustically.

• Harmonic oscillatorBroader topic: It is the motion produced by an ideal harmonic oscillator.

• TrigonometryRelated: Sine and cosine describe its position and velocity over time.

• DisplacementBroader topic: Displacement from equilibrium determines the restoring acceleration.

• OscillationBroader topic: It is the ideal pattern produced by a linear restoring force.

• CosineRelated: Its displacement can be modeled by a cosine function of time.

• Circular motionCompared with: It can be modeled as the projection of uniform circular motion onto a diameter.

• Uniform circular motionRelated: The projection of uniform circular motion onto one axis produces simple harmonic motion.

• Periodic orbitBroader topic: Its sinusoidal trajectories are elementary periodic orbits.

• Small-angle approximationRelated: Replacing sin θ with θ turns the pendulum’s angular equation into a linear oscillator model.

• Angular displacementRelated: Rotating phasors use angular displacement to represent the phase of oscillations.

• Longitudinal waveRelated: Small-amplitude particles in many longitudinal waves approximately follow this motion.

• Damped harmonic oscillatorNarrower topic: Removing dissipation from this motion gives the undamped oscillator.

• Mechanical energyRelated: Its energy repeatedly shifts between kinetic and potential forms.

• Simple pendulumNarrower topic: At small amplitudes, the simple pendulum is a physical example of this general motion.

• Angular accelerationRelated: A torsional oscillator's changing angular acceleration follows the same restoring pattern.

• Second derivativeRelated: Its defining equation relates position directly to its second derivative.

• Sine and cosineRelated: Its position can be expressed as a sine or cosine function of time.

• Mechanical resonanceNarrower topic: It is the idealized free motion underlying the basic resonant oscillator.

• Period (time interval)Broader topic: Its period can be calculated from the system’s restoring force and inertia.

• Radian per secondRelated: Its angular frequency, measured in radians per second, sets the oscillation timescale.

• Restoring forceRelated: A restoring force proportional to displacement produces this characteristic motion.

• Instantaneous velocityBroader topic: Its velocity varies continuously and becomes zero at the turning points.

• Rocking horseRelated: Small rocking movements can approximate this familiar oscillation pattern.

• DashpotRelated: Adding a dashpot changes undamped oscillation into damped motion.

• Differentiation of trigonometric functionsRelated: Sine and cosine derivatives connect displacement, velocity, and acceleration.

• Newtonian dynamicsBroader topic: Newton’s laws derive the oscillations of ideal springs and pendulums at small angles.