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Below is a table showing analogous quantities in four harmonic oscillator systems in mechanics and electronics. If analogous parameters on the same line in the table are given numerically equal values, the behavior of the oscillators – their output waveform, resonant frequency, damping factor, etc. – are the same.
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.
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 the spring-mass system, oscillations occur because, at the static equilibrium displacement, the mass has kinetic energy which is converted into potential energy stored in the spring at the extremes of its path. The spring-mass system illustrates some common features of oscillation, namely the existence of an equilibrium and the presence of a ...
This discussion applies the following simplifications: the spring itself is taken as being weightless, and the spring is taken as being a perfect spring; the restoring force increases in a linear way as the spring is stretched out. That is, the restoring force is exactly proportional to the distance from the center of rotation.
The displacement of an undamped spring-mass system oscillating around the equilibrium over time is a sine wave. Sinusoids that exist in both position and time also have: a spatial variable x {\displaystyle x} that represents the position on the dimension on which the wave propagates.
A Wilberforce pendulum can be designed by approximately equating the frequency of harmonic oscillations of the spring-mass oscillator f T, which is dependent on the spring constant k of the spring and the mass m of the system, and the frequency of the rotating oscillator f R, which is dependent on the moment of inertia I and the torsional ...
The model is derived by modeling an electron orbiting a massive, stationary nucleus as a spring-mass-damper system. [2] [3] [4] The electron is modeled to be connected to the nucleus via a hypothetical spring and its motion is damped by via a hypothetical damper. The damping force ensures that the oscillator's response is finite at its ...