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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.
For this reason, the in-line slider-crank mechanism produces balanced motion. This balanced motion implies other ideas as well. Assuming the crank arm is driven at a constant velocity, the time it takes to perform a forward stroke is equal to the time it takes to act a reverse stroke. The crank moves in only one direction, provided the position ...
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 = /, the time for a single oscillation or its frequency = /, the number of cycles per unit time.
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 location of the piston versus time is simple harmonic motion, i.e., a sine wave having constant amplitude and constant frequency, given a constant rotational speed. Comparison of displacement and acceleration for a Scotch yoke compared with a crank and slider
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
Even a simple harmonograph as described can create ellipses, spirals, figure eights and other Lissajous figures. More complex harmonographs incorporate three or more pendulums or linked pendulums together (for example, hanging one pendulum off another), or involve rotary motion, in which one or more pendulums is mounted on gimbals to allow ...
When the different harmonic components in the system are in phase, the resulting trajectory is simple and periodic, such as the "smile" trajectory, which resembles that of an ordinary pendulum, and various loops. [3] [8] In general a periodic orbit exists when the following is satisfied: [1]