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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.
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 direction oppose the deformation.
As the absolute value of x increases, so does the restoring force acting on the pendulums weight that pushes it back towards its resting position. In harmonic oscillators, the restoring force is proportional in magnitude (and opposite in direction) to the displacement of x from its natural position x 0.
Due to frictional force, the velocity decreases in proportion to the acting frictional force. While in a simple undriven harmonic oscillator the only force acting on the mass is the restoring force, in a damped harmonic oscillator there is in addition a frictional force which is always in a direction to oppose the motion.
The homotopy analysis method (HAM) has also been reported for obtaining approximate solutions of the Duffing equation, also for strong nonlinearity. [ 4 ] [ 5 ] In the special case of the undamped ( δ = 0 {\displaystyle \delta =0} ) and undriven ( γ = 0 {\displaystyle \gamma =0} ) Duffing equation, an exact solution can be obtained using ...
Tension (as a transmitted force, as an action-reaction pair of forces, or as a restoring force) is measured in newtons in the International System of Units (or pounds-force in Imperial units). The ends of a string or other object transmitting tension will exert forces on the objects to which the string or rod is connected, in the direction of ...
The motion of the circling masses mapped in a coordinate system that is rotating at a constant angular velocity Harmonic oscillation the restoring force is proportional to the distance from the center. The animation on the right provides a clearer view on the oscillation of the angular velocity. There is a close analogy with harmonic oscillation.
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.