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In physics and mathematics, in the area of dynamical systems, an elastic pendulum [1] [2] (also called spring pendulum [3] [4] or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system. [2]
A mass m attached to a spring of spring constant k exhibits simple harmonic motion in closed space. The equation for describing the period: = shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small. The above equation is also valid in the case when an additional constant force is being ...
A balance wheel, or balance, is the timekeeping device used in mechanical watches and small clocks, analogous to the pendulum in a pendulum clock.It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral torsion spring, known as the balance spring or hairspring.
When a spring is stretched or compressed by a mass, the spring develops a restoring force. Hooke's law gives the relationship of the force exerted by the spring when the spring is compressed or stretched a certain length: F ( t ) = − k x ( t ) , {\displaystyle F(t)=-kx(t),} where F is the force, k is the spring constant, and x is the ...
A balance spring, or hairspring, is a spring attached to the balance wheel in mechanical timepieces. It causes the balance wheel to oscillate with a resonant frequency when the timepiece is running, which controls the speed at which the wheels of the timepiece turn, thus the rate of movement of the hands.
Notice =, a homogeneous rod oscillates as if it were a simple pendulum of two-thirds its length. A heavy simple pendulum: combination of a homogeneous rod of mass m r o d {\displaystyle m_{\mathrm {rod} }} and length ℓ {\displaystyle \ell } swinging from its end, and a bob m b o b {\displaystyle m_{\mathrm {bob} }} at the other end.
Some trajectories of a harmonic oscillator according to Newton's laws of classical mechanics (A–B), and according to the Schrödinger equation of quantum mechanics (C–H). ). In A–B, the particle (represented as a ball attached to a spring) oscillates back and fo
A mass suspended by a spring is the classical example of a harmonic oscillator A mass m attached to the end of a spring is a classic example of a harmonic oscillator . By pulling slightly on the mass and then releasing it, the system will be set in sinusoidal oscillating motion about the equilibrium position.