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In mechanics and physics, simple harmonic motion (sometimes abbreviated as SHM) is a special type of periodic motion an object experiences by means of a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position.
A simple pendulum exhibits approximately simple harmonic motion under the conditions of no damping and small amplitude. Assuming no damping, the differential equation governing a simple pendulum of length l {\displaystyle l} , where g {\displaystyle g} is the local acceleration of gravity , is d 2 θ d t 2 + g l sin θ = 0. {\displaystyle ...
The restoring force is often referred to in simple harmonic motion. The force responsible for restoring original size and shape is called the restoring force. [1] [2] An example is the action of a spring. An idealized spring exerts a force proportional to the amount of deformation of the spring from its equilibrium length, exerted in a ...
The systems where the restoring force on a body is directly proportional to its displacement, such as the dynamics of the spring-mass system, are described mathematically by the simple harmonic oscillator and the regular periodic motion is known as simple harmonic motion.
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; Keplers laws of planetary motion (in physics, known as the ...
Diagram showing the periodic orbit of a mass-spring system in simple harmonic motion. (Here the velocity and position axes have been reversed from the standard convention in order to align the two diagrams) Given a dynamical system (T, M, Φ) with T a group, M a set and Φ the evolution function
A simple interpretation of Hamiltonian mechanics comes from its application on a one-dimensional system consisting of one nonrelativistic particle of mass m. The value H ( p , q ) {\displaystyle H(p,q)} of the Hamiltonian is the total energy of the system, in this case the sum of kinetic and potential energy , traditionally denoted T and V ...
An example of a time-independent Hamiltonian system is the harmonic oscillator. ... to initial conditions, and the motion appears random and erratic, the system is ...