This model applies to a single point particle constrained to move in one dimension whose position is a sinusoidal function of time. Simple harmonic motion is sometimes abbreviated SHM.

Any object that experiences a linear restoring force or torque so that the equation of motion takes the form

or

will experience simple harmonic motion with angular frequency ω. The prototypical example is an object of mass m attached to a spring with force constant k, in which case, by [Hooke's Law]:

giving simple harmonic motion with angular frequency

In the real world, most situations in which there is a stable position with a restoring force can be treated (for small oscillations at least) as if the restoring force is linear. Therefore, even systems with non-ideal springs and the oscillations of a pendulum can be treated as cases of Simple Harmonic Motion as long as the motion is small.

Another cue that Simple Harmonic Motion is occurring is if the poision, the velocity, or the acceleration are sinusoidal in time.

.

• 1-D Motion (Constant Velocity)
• 1-D Motion (Constant Acceleration)
• [Mechanical Energy and Non-Conservative Work]

• restoring force
• periodic motion
• angular frequency
• phase

A single point particle (or, for the angular version of SHM, a single rigid body).

The system must be subject to a one-dimensional restoring force (or torque) that varies linearly with the displacement (or angular displacement) from an equilibrium position.

• Acceleration versus time graph.
• Velocity versus time graph.
• Position versus time graph.