# Oscillators Definition and 6 Discussions

Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.
Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.

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1. ### Energy conservation: electromagnetic wave in matter

Hi, I completely failed this homework. I mean I think I know what happen, but I don't know how to show it mathematically. The energy lost by the wave is used to oscillate the electrons inside the conductor. Thus, the electrons acts like some damped driven oscillators. I guess I have to find...
2. ### Induction heater

Hello; I am trying to come up with an induction heater design for a machine that i am working on and am having some trouble planning it out. Anybody have some good resources? I have scoured Google and there are tons on there. I am a bit unsure how to get started. I have an induction heater...
3. ### Avalanche relaxation oscillator biasing resistor

I've tried the circuit in this article. It works very well and I've obtained 2ns clear pulses at 150 V (the main issue was to find the right avalanche voltage, which turned out to be 150-160V for my 2n3904 transistor). While the basic principles of operation in this circuit is clear for me, I...
4. ### Perturbation on an oscillator

Hi, I am reading the Hajimiri-Lee phase noise model, and got a question on that. If you have an LC tank circuit that is free-running and I inject a current i(t) (dirac current) at instants either t1 or t2 (shown in the figure), depending on when you inject the phase of the output changes (as...
5. ### I Why high Q factors have low phase noise

If we define Q factor as 2*pi* energy stored/ energy dissipated per cycle, what's the physical insight behind obtaining low phase noise for oscillators when we have high Q factors? (I know the mathematical derivation based on finding the frequency profile of an oscillator (like LC oscillator)...
6. ### Weak Damping - how to relate the amplitude and phase difference

Homework Statement Derive the relationship bewteen x_{max}, A_{+}, A_{-} and \phi Homework Equations x(t) = e^{\gamma t}(A_{+}e^{i \omega_d t} + A_{-}e^{-i \omega_d t}) x(t) = x_{max} e^{\gamma t} cos(\omega_d t + \phi) The Attempt at a Solution I know the e^{\gamma t} cancels and for the...