Examples of Under Damped in the following topics:
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- A door shutting thanks to an under damped spring would sway in the door way, briefly continuing to open and close.
- Let the damping force be proportional to the mass' velocity by a proportionality constant, b, called the vicious damping coefficient.
- The physical situation has three possible results depending on the value of a, which depends on the value of what is under our radical.
- $\gamma^2 > 4\omega_0^2$ is the Over Damped case.
- $\gamma^2 < 4\omega_0^2$ is the Under Damped case.
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- The fluid will damp out the motion, more or less depending on whether it has the viscosity of water or honey.
- This looks like the equation of a damped sinusoid.
- First if $\frac{\gamma}{2\omega_0} < 1$ , corresponding to small damping, then the argument of the square root is positive and indeed we have a damped sinusoid.
- In this case the motion is said to be "over-damped" since there is no oscillation.
- The borderline case $\gamma = 2 \omega_0$ is called critical damping, in which case $x(t) = x_0 e^{-\frac{\gamma}{2} t}$ .
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- At first the finger is held steady, and the ball bounces up and down with a small amount of damping.
- In real life, most oscillators have damping present in the system.
- It is interesting that the widths of the resonance curves shown in depend on damping: the less the damping, the narrower the resonance.
- The more selective the radio is in discriminating between stations, the smaller its damping.
- The narrowest response is also for the least amount of damping.
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- Driven harmonic oscillators are damped oscillators further affected by an externally applied force.
- If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator.
- Driven harmonic oscillators are damped oscillators further affected by an externally applied force F(t).
- \omega_0$, and the damping ratio $\!
- Describe a driven harmonic oscillator as a type of damped oscillator
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- Back EMF, eddy currents, and magnetic damping are all due to induced EMF and can be explained by Faraday's law of induction.
- Eddy currents can produce significant drag, called magnetic damping, on the motion involved.
- A common physics demonstration device for exploring eddy currents and magnetic damping.
- (c) There is also no magnetic damping on a nonconducting bob, since the eddy currents are extremely small.
- Explain the relationship between the motional electromotive force, eddy currents, and magnetic damping
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- The causes of damping are extremely subtle.
- Try extending a damping piston of the sort used on doors.
- where $\gamma$ is a constant reflecting the strength of the damping.
- \label{damping} }$
- Square of the amplitude factor for forced, damped motion near a resonance $\omega_0$.
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- The shock absorber is analogous to the resistance damping and limiting the amplitude of the oscillation.
- The forced but damped motion of the wheel on the car spring is analogous to an RLC series AC circuit.
- The shock absorber damps the motion and dissipates energy, analogous to the resistance in an RLC circuit.
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- That's just under 1.3 oscillations per second, or 1.3 Hz.
- Thus the total force on the mass (spring + gravity, but no damping for now) is mg $- k(\Delta l + x)$.
- So far we have not accounted for the damping of the spring.
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- For the characteristic frequency you estimated above, what is the minimum damping required to ensure that the mass does not oscillate if you pull it down and let it go.
- With this minimum (or "critical") damping, how long will it take for the mass to come to rest?
- (a) What is the damping constant ( $\gamma$ ) for the circuit?
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- Free oscillations are also called transients since for any real system in the absence of a forcing term, the damping will cause the motion to die out.