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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.
In physics, the restoring force is a force that acts to bring a body to its equilibrium position. The restoring force is a function only of position of the mass or particle, and it is always directed back toward the equilibrium position of the system. The restoring force is often referred to in simple harmonic motion.
In the experiment, mechanical waves traveled in opposite directions form immobile points, called nodes. These waves were called standing waves by Melde since the position of the nodes and loops (points where the cord vibrated) stayed static. Standing waves were first discovered by Franz Melde, who coined the term "standing wave" around 1860.
Spatial position Position of a point in space, not necessarily a point on the wave profile or any line of propagation d, r: m [L] Wave profile displacement Along propagation direction, distance travelled (path length) by one wave from the source point r 0 to any point in space d (for longitudinal or transverse waves) L, d, r
The position at a given time t also depends on the phase φ, which determines the starting point on the sine wave. The period and frequency are determined by the size of the mass m and the force constant k , while the amplitude and phase are determined by the starting position and velocity .
A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back towards the equilibrium position.
In the position representation, this is the first-order differential equation (+) =, whose solution is easily found to be the Gaussian [nb 1] =. Conceptually, it is important that there is only one solution of this equation; if there were, say, two linearly independent ground states, we would get two independent chains of eigenvectors for the ...
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.