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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 ...
In addition, an oscillating system may be subject to some external force, as when an AC circuit is connected to an outside power source. In this case the oscillation is said to be driven. The simplest example of this is a spring-mass system with a sinusoidal driving force.
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 mass m attached to a spring of spring constant k exhibits simple harmonic motion in closed space. The equation for describing the period: T = 2 π m k {\displaystyle T=2\pi {\sqrt {\frac {m}{k}}}} shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small.
For a single damped mass-spring system, the Q factor represents the effect of simplified viscous damping or drag, where the damping force or drag force is proportional to velocity. The formula for the Q factor is: Q = M k D , {\displaystyle Q={\frac {\sqrt {Mk}}{D}},\,} where M is the mass, k is the spring constant, and D is the damping ...
Natural frequency, measured in terms of eigenfrequency, is the rate at which an oscillatory system tends to oscillate in the absence of disturbance. A foundational example pertains to simple harmonic oscillators, such as an idealized spring with no energy loss wherein the system exhibits constant-amplitude oscillations with a constant frequency.
Underdamped spring–mass system with ζ < 1. In physical systems, damping is the loss of energy of an oscillating system by dissipation. [1] [2] Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. [3]
where m is the mass and k is the spring constant. For a given mass, stiffening the system (increasing ) increases its natural frequency, which is a general characteristic of vibrating mechanical systems. A swing set is another simple example of a resonant system with which most people have practical experience. It is a form of pendulum.