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An undamped spring–mass system is an oscillatory system. Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states.
The motion is periodic, repeating itself in a sinusoidal fashion with constant amplitude A. In addition to its amplitude, the motion of a simple harmonic oscillator is characterized by its period T = 2 π / ω {\displaystyle T=2\pi /\omega } , the time for a single oscillation or its frequency f = 1 / T {\displaystyle f=1/T} , the number of ...
Thus simple harmonic motion is a type of periodic motion. If energy is lost in the system, then the mass exhibits 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.
Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period. For a function on the real numbers or on the integers , that means that the entire graph can be formed from copies of one particular portion, repeated at regular intervals.
Harmonic motion can mean: the displacement of the particle executing oscillatory motion that can be expressed in terms of sine or cosine functions known as harmonic motion . The motion of a Harmonic oscillator (in physics), which can be: Simple harmonic motion; Complex harmonic motion
Vibration (from Latin vibrāre 'to shake') is a mechanical phenomenon whereby oscillations occur about an equilibrium point.Vibration may be deterministic if the oscillations can be characterised precisely (e.g. the periodic motion of a pendulum), or random if the oscillations can only be analysed statistically (e.g. the movement of a tire on a gravel road).
The motion of an ensemble of systems in this space is studied by classical statistical mechanics. The local density of points in such systems obeys Liouville's theorem, and so can be taken as constant. Within the context of a model system in classical mechanics, the phase-space coordinates of the system at any given time are composed of all of ...
An oscillator is a physical system characterized by periodic motion, such as a pendulum, tuning fork, or vibrating diatomic molecule.Mathematically speaking, the essential feature of an oscillator is that for some coordinate x of the system, a force whose magnitude depends on x will push x away from extreme values and back toward some central value x 0, causing x to oscillate between extremes.