Editing Oscillation (section)

==Simple harmonic oscillation==
{{Main|Simple harmonic motion}}

The simplest mechanical oscillating system is a [[weight]] attached to a [[linear]] [[spring (device)|spring]] subject to only [[weight]] and [[Tension (physics)|tension]].  Such a system may be approximated on an air table or ice surface.  The system is in an [[mechanical equilibrium|equilibrium]] state when the spring is static. If the system is displaced from the equilibrium, there is a net ''restoring force'' on the mass, tending to bring it back to equilibrium.  However, in moving the mass back to the equilibrium position, it has acquired [[momentum]] which keeps it moving beyond that position, establishing a new restoring force in the opposite sense.  If a constant [[force]] such as [[gravity]] is added to the system, the point of equilibrium is shifted.  The time taken for an oscillation to occur is often referred to as the oscillatory ''period''.

The systems where the restoring force on a body is directly proportional to its displacement, such as the [[dynamics (mechanics)|dynamics]] of the spring-mass system, are described mathematically by the [[Harmonic oscillator#Simple harmonic oscillator|simple harmonic oscillator]] and the regular [[period (physics)|periodic]] motion is known as [[simple harmonic motion]].  In the spring-mass system, oscillations occur because, at the [[statics|static]] equilibrium displacement, the mass has [[kinetic energy]] which is converted into [[potential energy]] stored in the spring at the extremes of its path.  The spring-mass system illustrates some common features of oscillation, namely the existence of an equilibrium and the presence of a restoring force which grows stronger the further the system deviates from equilibrium.

In the case of the spring-mass system, [[Hooke's law]] states that the restoring force of a spring is:
<math display="block">F = -kx</math>

By using [[Newtons second law|Newton's second law]], the differential equation can be derived:
<math display="block">\ddot{x} = -\frac km x = -\omega^2 x,</math>
where <math display="inline">\omega = \sqrt{k/m}</math>

The solution to this differential equation produces a sinusoidal position function:
<math display="block">x(t) = A \cos (\omega t - \delta)</math>

where {{mvar|ω}} is the frequency of the oscillation, {{mvar|A}} is the amplitude, and {{mvar|δ}} is the [[phase shift]] of the function. These are determined by the initial conditions of the system. Because cosine oscillates between 1 and −1 infinitely, our spring-mass system would oscillate between the positive and negative amplitude forever without friction.