All Questions
Tagged with harmonic-oscillator friction
63
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If friction is not proportional to velocity, why do we model it as such when considering damped oscillations? [duplicate]
Early in our study of mechanics, we learn that friction is usually proportional only to normal force, without dependence on velocity. However, during our studies of damped oscillations, we often model ...
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Maxwell's wheel - moment of inertia vs damping coeff
I am investigating the relationship between the moment of inertia of a yoyo-like apparatus (maxwell's wheel) and its damping coeff. I am adding disks to my yoyo to change its moment of inertia, which ...
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Critical damping and mathematical requirement of 2 constants
The general equation of an oscillator with a damping term $-rv$, where $r$ is damping coeffeciet and $v$ is velocity is
$$x=e^{-pt}(Ae^{qt}+Be^{-qt})$$
where $p=r/2m$ and $q=\sqrt{p^2-s/m}$, $s$ is ...
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Generalizing the damped harmonic oscillator equation to 3D
I am way out of my depth here so bear with me. I haven't done any physics in a few years so my memory is rusty.
The equation for a damped harmonic oscillator is:
$$x(t) = A\exp(-bt/2m)\cos(ω*t + \phi)$...
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Deriving the Exponential Decay Rate in Damped Oscillation
I am currently working on this book: https://openstax.org/books/university-physics-volume-1/pages/15-5-damped-oscillations
The position as a function of time for damped oscillations is given by $$x(t)=...
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In a damped harmonic oscillator, what exactly is $b$ in the equation $F_{damping}=-bv$, and does it ever change?
Does $b$ change as mass changes? I've experimented with a mass-spring system damped in water and recorded it using video tracking software. Using the Logger Pro's "Damped Harmonic Model Fit" ...
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Damped harmonic motion experiment, bad results but good statistics
I've done an experiment with a pendulum swinging at very small angles. I added an object with the shape of a rectangle to it, to increase the air friction to create damped harmonic motion.
This is the ...
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Mass of spring in damped harmonic motion
In my textbook, the equations for damped harmonic motion seem to neglect the mass of the spring. What would the equations look like if we actually included the mass of the spring? For example, we have ...
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Damping constant (damped harmonic motion)
For damped harmonic motion, the equation for the damping force is F=-bv where F is the damping force exerted on the object, v the velocity of the object and b the damping constant.
For an experiment, ...
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Damped harmonic motion
Pretend we have a mass which is attached to a vertical spring. If we were to extend the spring by dragging it down and then releasing it, the weight would start to oscillate. Because of friction from ...
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Can the damping coefficient of a pendulum be predicted given physical variables?
I'm aware you're able to calculate the coefficient of damping, $b$, given a set of amplitudes over time through $$\ln(\theta/\theta_0) = -bt/2$$ However, is there any way to get $b$ without empirical ...
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Hamilton's equations of motion for damped oscillator
Consider a parallel RLC oscillator. Kirchhoff's equations of motion are
$$
\ddot{\Phi} + \frac{1}{\tau}\dot{\Phi} + \omega_0^2 \Phi = 0
$$
where $\tau = RC$ and $\omega_0 = 1 / \sqrt{LC}$.
What is ...
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Critical damping oscilations - Equation in Fowles book
I'm not understanding a passage in the Fowles's book, seventh edition, equation 3.4.9.
I understood that, considering:
$x$ = position
$\gamma$ = damping factor
${w_0}^2$ = k/m, where k is the ...
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Non-conservative force, but equation of harmonic motion
A small disc is projected on a horizontal floor with speed $u$. Coefficient of friction between the disc and floor varies as $\mu = \mu_0+ kx$, where $x$ is the distance covered. Find distance slid by ...
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Intuition behind the differential equation for forced oscillations
The differential equation for forced oscillation is:
$$m \ddot{x} + b\dot{x}+kx = F_{o}\sin(\omega''t)$$
I don't find this equation intuitively satisfying. My mind tends to think that as $F_{o}\sin(\...
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