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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 ...
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.
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.
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]
The mass of the cart and the point mass at the end of the rod are denoted by M and m. The rod has a length l. The pendulum is assumed to consist of a point mass, of mass , affixed to the end of a massless rigid rod, of length , attached to a pivot point at the end opposite the point mass.
The spring-mass system illustrates some common features of oscillation, namely the existence of an equilibrium and the presence of a restoring force which grows stronger the further the system deviates from equilibrium. In the case of the spring-mass system, Hooke's law states that the restoring force of a spring is: =
The effective mass of the spring in a spring-mass system when using a heavy spring (non-ideal) of uniform linear density is of the mass of the spring and is independent of the direction of the spring-mass system (i.e., horizontal, vertical, and oblique systems all have the same effective mass). This is because external acceleration does not ...