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For example, landing a plane in autopilot: if the system overshoots and releases landing gear too late, the outcome would be a disaster. Critically damped The case where = is the border between the overdamped and underdamped cases, and is referred to as critically damped. This turns out to be a desirable outcome in many cases where engineering ...
Plot showing underdamped and overdamped responses of a series RLC circuit to a voltage input step of 1 V. The critical damping plot is the bold red curve. The plots are normalised for L = 1, C = 1 and ω 0 = 1. The differential equation has the characteristic equation, [7] + + =.
An underdamped response is one that oscillates within a decaying envelope. The more underdamped the system, the more oscillations and longer it takes to reach steady-state. Here damping ratio is always less than one. Critically damped A critically damped response is the response that reaches the steady-state value the fastest without being ...
In real oscillators, friction, or damping, slows the motion of the system. Due to frictional force, the velocity decreases in proportion to the acting frictional force. While in a simple undriven harmonic oscillator the only force acting on the mass is the restoring force, in a damped harmonic oscillator there is in addition a frictional force ...
In physics, complex harmonic motion is a complicated realm based on the simple harmonic motion.The word "complex" refers to different situations. Unlike simple harmonic motion, which is regardless of air resistance, friction, etc., complex harmonic motion often has additional forces to dissipate the initial energy and lessen the speed and amplitude of an oscillation until the energy of the ...
The Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...
A phase portrait graph of a dynamical system depicts the system's trajectories (with arrows) and stable steady states (with dots) and unstable steady states (with circles) in a phase space. The axes are of state variables.
If the system is overdamped, then the waveform may never actually reach the theoretical high and low levels, and if the system is underdamped, it will oscillate about the high and low levels before settling down. In these cases, the rise and fall times are measured between specified intermediate levels, such as 5% and 95%, or 10% and 90%.