Editing Simple harmonic motion (section)

==Introduction==
The motion of a [[particle]] moving along a straight line with an [[acceleration]] whose direction is always toward a [[fixed point (mathematics)|fixed point]] on the line and whose magnitude is proportional to the displacement from the fixed point is called simple harmonic motion.<ref>{{cite web |title=Simple Harmonic Motion – Concepts |url=https://www.webassign.net/question_assets/ncsucalcphysmechl3/lab_7_1/manual.html}}</ref>

In the diagram, a [[harmonic oscillator|simple harmonic oscillator]], consisting of a weight attached to one end of a spring, is shown. The other end of the spring is connected to a rigid support such as a wall. If the system is left at rest at the [[mechanical equilibrium|equilibrium]] position then there is no net [[force]] acting on the mass. However, if the mass is displaced from the equilibrium position, the spring [[exertion|exerts]] a restoring [[elasticity (physics)|elastic]] force that obeys [[Hooke's law]].

Mathematically,
<math display="block"> \mathbf{F}=-k\mathbf{x}, </math>
where {{math|'''F'''}} is the restoring elastic force exerted by the spring (in [[International System of Units|SI]] units: [[newton (unit)|N]]), {{math|''k''}} is the [[Hooke's law|spring constant]] ([[newton (unit)|N]]·m<sup>−1</sup>), and {{math|'''x'''}} is the [[displacement (vector)|displacement]] from the equilibrium position (in [[metre]]s).

For any simple mechanical harmonic oscillator:
*When the system is displaced from its equilibrium position, a restoring force that obeys Hooke's law tends to restore the system to equilibrium.

Once the mass is displaced from its equilibrium position, it experiences a net restoring force. As a result, it [[acceleration|accelerates]] and starts going back to the equilibrium position. When the mass moves closer to the equilibrium position, the restoring force decreases. At the equilibrium position, the net restoring force vanishes. However, at {{math|''x'' {{=}} 0}}, the mass has [[momentum]] because of the acceleration that the restoring force has imparted. Therefore, the mass continues past the equilibrium position, compressing the spring. A net restoring force then slows it down until its [[velocity]] reaches zero, whereupon it is accelerated back to the equilibrium position again.

As long as the system has no [[energy]] loss, the mass continues to oscillate. Thus simple harmonic motion is a type of [[frequency|periodic]] motion. If energy is lost in the system, then the mass exhibits [[damped oscillator|damped oscillation]].

Note if the real space and [[phase space]] plot are not co-linear, the phase space motion becomes elliptical. The area enclosed depends on the amplitude and the maximum momentum.