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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 ...
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]
Coupled pendulums can affect each other's motion, either through a direction connection (such as a spring connecting the bobs) or through motions in a supporting structure (such as a tabletop). The equations of motion for two identical simple pendulums coupled by a spring connecting the bobs can be obtained using Lagrangian mechanics.
A simple harmonic oscillator is an oscillator that is neither driven nor damped.It consists of a mass m, which experiences a single force F, which pulls the mass in the direction of the point x = 0 and depends only on the position x of the mass and a constant k.
The stiffness of the spring, its spring coefficient, in N·m/radian^2, along with the balance wheel's moment of inertia, in kg·m 2, determines the wheel's oscillation period. The equations of motion for the balance are derived from the angular form of Hooke's law and the angular form of Newton's second law: τ = − κ θ = I α ...
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
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This is because external acceleration does not affect the period of motion around the equilibrium point. The effective mass of the spring can be determined by finding its kinetic energy. For a differential mass element of the spring d m {\displaystyle \mathrm {d} m} at a position s {\displaystyle s} (dummy variable) moving with a speed u ( s ...