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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 ...
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 a mass–spring system, with mass m and spring stiffness k, the natural angular frequency can be calculated as: = In an electrical network , ω is a natural angular frequency of a response function f ( t ) if the Laplace transform F ( s ) of f ( t ) includes the term Ke − st , where s = σ + ω i for a real σ , and K ≠ 0 is a constant ...
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 ...
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 ...
A spring that obeys Hooke's Law with spring constant k will have a total system energy E of: [14] = Here, A is the amplitude of the wave-like motion that is produced by the oscillating behavior of the spring.
With a real spring there is friction involved. With a real spring the vibration will be damped and the final situation will be that the masses circle each other at a constant distance, with a constant tension of the spring.