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Lab #11: Simple Harmonic Motion of a Linear Oscillator
Lab #11: Simple Harmonic Motion of a Linear Oscillator

... When resonance occurs, the amplitude, xm, of the system reaches a maximum. There are many examples of resonance in everyday life. Engineers must be extremely careful not to design a structure that has a natural frequency that matches a potential driving force. The Tacoma Narrows Bridge disaster is a ...
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... The friction in an oscillating system is referred to as damping. When a damped oscillator is given a nonzero displacement at t = 0 and released, it can exhibit three different types of behavior: (1) overdamped (2) critically damped (3) underdamped ...
Ordinary Differential Equations
Ordinary Differential Equations

Chapter1. OSCILLATIONS
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... the system is said to be underdamped. As the value of b increases, the amplitude of the oscillations decreases more and more rapidly  When b reaches a critical value bc such that bc/2m = w0, the system does not oscillate and is said to be critically damped. In this case the system, once released fr ...
Oscillations (PPT) - Uplift North Hills Prep
Oscillations (PPT) - Uplift North Hills Prep

...  It also tells us that if the displacement x is negative (left), the spring force F is positive (right).  Any force that acts in the direction opposite to displacement , pointing always toward equilibrium, trying to restore system back to equilibrium is called a restoring force. In addition to tha ...
PY231: Notes on Linear and Nonlinear Oscillators, and Periodic
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... We now ask: “What happens when we start driving an oscillator?” In musical terms, this is equivalent to asking what happens when a brass player begins a note. There are two possibilities: The player can have the lips vibrating at exactly the same frequency as the air column wants to vibrate with, or ...
Physics 201: Lecture 1
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... If Fmax = bvmax < kA, the system is said to be underdamped When b reaches a critical value bc such that bc / 2 m =  0 , the system will not oscillate  The system is said to be critically damped If Fmax = bvmax > kA and b/2m >  0, the system is said to be overdamped ...
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... A pendulum is launched in two different ways. During both launches, the bob is given an initial speed 3 m/s and the same initial angle from vertical. Which launch will cause the pendulum to swing the largest angle from the equilibrium position to the left side? A) Launch 1 B) Launch 2 C) Both are th ...
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Harmonic Motion, Waves, and Sound Wave Models

... between 20 and 20,000 hertz, but the actual range that is heard varies with each individual. Students discover this by measuring their own sensitivity to sound as well as the sensitivity of their classmates. In the process, students learn how to design an unbiased experiment. ...
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... of damping force, but friction is one common source. There can be air resistance or resistance at the fixed hinge from which oscillating part is hung. It is imperative that we supply appropriate energy (force) to compensate for the loss of energy due to damping. To meet this requirement, the oscilla ...
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... Detecting the oscillations of micrometer- and nanometerscale mechanical resonators [1,2] is an important component of many applications and fundamental measurements involving these devices. Most commonly, optical techniques are employed, providing very high sensitivities. These techniques can be imp ...
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... phases of two constituent waves are lined up so that they reinforce. The minimum amplitude is |A−B | (= � 0) and it occurs when the two waves are perfectly out of sync and experience destructive interference. Beats have applications in tuning musical instruments or radar technology. If a tuning ins ...
Potential Energy - McMaster University
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... • An oscillator driven by an external periodic force will oscillate with an amplitude that depends on the driving frequency. The amplitude is large when the driving frequency is close to the “natural” frequency of the oscillator. •For weak damping, the system oscillates, and the amplitude decreases ...
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Oscillations and Periodic Motion

(c) Damped forced vibration – applied force
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... Once again, we see that a driving frequency near to the natural frequency produces rather critical conditions, and if excessive amplitudes are to be avoided, then driving the system close to its resonant frequency is to be avoided. This means that either the system should be driven at a different fr ...
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Optical heterodyne detection

Optical heterodyne detection is the implementation of heterodyne detection principle using a nonlinear optical process. In heterodyne detection, a signal of interest at some frequency is non-linearly mixed with a reference ""local oscillator"" (LO) that is set at a close-by frequency. The desired outcome is the difference frequency, which carries the information (amplitude, phase, and frequency modulation) of the original higher frequency signal, but is oscillating at a lower more easily processed carrier frequency.Optical heterodyne detection has special temporal and spatial characteristics that pragmatically distinguish it from conventional Radio Frequency(RF) heterodyne detection. Electrical field oscillations in the optical frequency range cannot be directly measured since the relatively high optical frequencies have oscillating fields that are much faster than electronics can respond. Instead, optical photons are detected by energy or equivalently by photon counting, which are proportional to the square of the electric field and thus form a non-linear event. Thus when the LO and the signal beams impinge together on the surface of a photodiode they ""mix"", producing heterodyne beat frequencies directly via the physics of energy absorption. While an old technique, key limiting issues were solved only as recently as 1994 with the invention of synthetic array heterodyne detection.
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