Questions tagged [dissipation]

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Virial theorem for two particle inelastic collision

Consider two point masses separated by a large distance R so that their initial potential energy can be considered 0. They are both at rest with respect to the Centre of Mass (COM) reference frame so ...
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33 views

Can light travel in closed loops indefinitely? [closed]

For simplicity, consider the two dimensional space. My question is that can there be a refractive index $(x, y)\mapsto n(x, y)$ such that the there is at least one closed permissible path (which can ...
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Overdamped dynamics and minimization principles

Most physicists are familiar with Hamilton's principle, which allows us to derive the equations of classical mechanics from the principle of stationary action, $$\delta S=0.\tag{1}$$ At the same time, ...
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19 views

Conservative vs Dissipative Forces

I will be speaking very loosely since I am not a physicist. Say a system evolves via a dissipative force, then usually as time moves on some energy functional will be decreasing. If a system has both ...
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1answer
40 views

Where did the boundary conditions go in the frequency-space solution to the Green's function for a damped harmonic oscillator?

In differential equations, Green's functions are only defined given boundary conditions. In fact, you need two of them for a second order differential equation. In a lot of physics lecture notes, a ...
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How to derive the response function of $m\ddot x + \gamma \dot x + kx = f$?

In a lecture on fluctuation-dissipation theorem, it is stated that EOM: $m\ddot x + \gamma \dot x + kx = f$ Response function $\chi(\omega) = (-m \omega^2 + i\gamma \omega + > k)^{-1}$ However, I ...
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35 views

When is static friction dissipative and when it is non-dissipative?

In some cases, like in pure rolling, static friction is non-dissipative in nature. So, how can we identify when is static friction dissipative or non-disspative?
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How do I account for damping on structural vibrations?

I want to know what terms to add to the differential equation for structural vibrations to account for structural damping. Not external damping, but internal damping. I consider the transfer of energy ...
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2answers
80 views

Why does an exact differential mean a force is conservative?

If you can express an integrand as an expression of just one variable i.e. $xdy + ydx = d(xy) = df$ then why does that mean that a loop integral on that will equal 0? Is it because if it is just a ...
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38 views

Energy dissipation due to displacement current

Consider the following problem: An isolated capacitor made of parallel circular plates of radius $a$ separated by a distance $d \gg a$ is charged such that there is a potential difference $V$ between ...
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1answer
32 views

Where to begin with the Rayleigh Dissipation Function?

I'm a final year student of mechanical engineering. Calculus of Variations isn't a part of our syllabus. I'm trying to understand the Rayleigh Dissipation function, and I understand that this is a ...
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Phase space for a damped harmonic oscillator [closed]

Given the equation $x''+2 \beta x'+ \omega^2 x=0$ for a damped oscillator, I can get to the equation of motion x(t) and deriving it with respect to time: $x'(t)$. I am asked to plot the phase plane $\...
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Why don't mirrors violate conservation of momentum/do they get warm? [duplicate]

Imagine you have a photon with momentum $p$ which hits a mirror $M$ and is reflected back. Since $M$ is at rest in your frame of reference the total momentum of the system pre-reflection is $p$ and ...
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Shaped Charge Physics

It seems that I have a problem understanding the physics behind shaped charge. I was told that shaped charges are the way they are because a hollow conical shape in the middle of an explosive will ...
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1answer
25 views

Resonance frequency of a guitar

I have some questions for you about the resonance phenomenon in a guitar: Why resonance frequency are only full integer multiples of the natural frequency, such as 2 x, 3 x, or 4 x or 3 x, 5 x, or 7 ...
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43 views

Is Bernoulli's principle applicable in viscous liquids?

I found very conflicting answers to this question. My textbook says viscosity is neglected for the derivation but it doesn't say anything about if it will still hold if viscosity is present. Another ...
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37 views

Reflection and transmission coefficient in Fresnel equations

If I have a look at the Fresnel equations on Wikipedia, I get the following expressions for reflection and transmission at perpendicular light incidence $$ R = \left|\frac{\hat n_1 - \hat n_2}{\hat ...
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Why can't we use conservation of mechanical energy here? [duplicate]

Consider a particle of mass $\text{m}$ fired from below into a bob of mass $\text{M}$ of a long, simple pendulum. The particle remains inside the bob and the bob rises through a height of $1.8\text{ m}...
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Is heat dissipation/heat loss a part of this Heat Generation formula?

I have been using a formula to calculate how much heat needs to be generated by a pipe in order to raise the temperature of the water flowing through the pipe by a certain amount, e.g. from $10^o$ C ...
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2answers
62 views

Does it always take the same amount of energy to get from A to B?

Imagine you have a point A and a point B. Does it takes the same amount of joules to travel from A to B no matter how you do it (if in neutral conditions e.g. no wind)? For example, walking, riding a ...
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Solving a classical damped free particle via the Fourier transform (and residue calculus)

Deriving the transfer function Suppose we have a free particle in one dimension with position $x$ and momentum $p$, and some damping $\Gamma$: \begin{equation} \begin{aligned} \dot{x} &= p/m, \\ \...
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35 views

Where does half of the work done in charging a capacitor is dissipated? [duplicate]

The energy stored in a charged capacitor of capacitance $C$ with $V$ voltage across it is: $$U= \frac 12 CV^2$$ Whereas the work done in charging the capacitor is: $$W= CV^2$$ This means that $(1/2)CV^...
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Contradiction? Getting a complex Fourier variable when solving the Helmholtz equation in lossy media

I want to find the general solution of the Helmholtz equation in the context of electromagentism $$(\nabla^2+n(\omega)^2\omega^2)\hat{E}(\omega, \vec{r})=0$$ For this I tried Fourier transforming the ...
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1answer
49 views

Help understanding forces in non-conservative systems

This might seem like a very simple problem, but it's stumping a few of us (myself obviously included). We have been tasked with showing the mechanical energy of a particle is dissipated under the ...
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2answers
249 views

Pendulum: how to measure the value of the decay constant $\tau$ experimentally?

I have been given the following function to model the behaviour of a simple physical pendulum: $$\theta(t) = \theta_o e^{-\frac{t}{\tau}} \cos\left(2\pi \frac{t}{T} + \alpha\right)$$ Where $\alpha$ is ...
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377 views

Can we lock the light (photons) up inside a box? Why / Why not? [duplicate]

Imagine a box designed to make vacuum state inside. Is it possible for us to lock the photons up inside something completely enclosed?
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36 views

How to calculate Complex Magnetic Impedance from Conductivity and Complex Permiability

For a week now I've been been racking my head trying to figure out how to calculate the Complex Magnetic Impedance of a material from its properties, namely Complex Permeability, and Conductivity. But ...
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1answer
76 views

A discrepancy on Wikipedia or a misunderstanding on my part?

Recently I have been trying to understand complex magnetic impedance and when I try to formulate the equations for it based off the similar equations for electrical circuits I keep coming up with some ...
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1answer
88 views

Damped harmonic Oscillator Lagrangian equivalence

The objective is to prove that the Lagrangian: $$L'=\frac{2\dot x+\lambda x}{2\Omega x}\tan^{-1}(\frac{2\dot x+\lambda x}{2\Omega x})-\frac{1}{2}\ln(\dot x^2+\lambda \dot{x } x + \omega^2x^2), \qquad \...
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Does a contracted spring become warm?

As far as I remember, if we stretch a solid iron bar mechanically, some portion of the work done by, say, the hydraulic pistons, makes the bar's temperature increase before it pulls apart. I want to ...
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106 views

Solutions to damped harmonic oscillator?

For the damped harmonic oscillator equation $$\frac{d^2x}{dt^2}+\frac{c}{m}\frac{dx}{dt}+\frac{k}{m}x=0$$ we get that the general solution is $$x(t)=Ae^{-\gamma t}e^{i\omega_d t}+Be^{-\gamma t}e^{-i\...
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1answer
42 views

Linearity of energy dissipation in a damped harmonic oscillator

Suppose we have a damped harmonic oscillator governed by $$m\ddot x +b \dot x + k x=F(t)$$ where $F$ is the force applied and $x$ is the response (displacement of the mass). Suppose the force $F=F_1+...
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Derivation of angular frequency of underdamped harmonic oscillator [closed]

Why is the angular frequency of an underdamped harmonic oscillator given by:$$\omega_1=\omega_0\sqrt{1-\zeta^2}$$
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1answer
56 views

How to prove that volume remains zero under a state transformation

The lecture note titled "11 Strange attractors and Lyapunov dim." taken from the book of Strogatz shows in eq(2) a coordinate transformation of the volume. I want to understand how to prove ...
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1answer
26 views

How does Conservation of Energy in hydroelectric power generation work?

In hydroelectric power generation, I've got a pretty good understanding for how kinetic energy from falling water is transformed into electrical energy. But when looking at the entire system, what ...
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48 views

Lagrange equations with friction with indirect velocity-dependency

I have a simple pendulum (a point-mass attached to a rigid massless rod) and want to model friction between the rod and the axis it's attached to. My assumption is that it can be modeled as surface ...
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3answers
64 views

Would it be possible to create a perpetual motion machine in an environment without air, friction, or dissipation?

Perpetual motion machines don't work because as it moves, the air molecules hit it and slow it down. Friction slows it down in a similar way. If there were no forces to slow it down, could it work?
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In what sense is a quantum damped harmonic oscillator dissipative?

The classical Hamiltonian of a damped harmonic oscillator $$H=\frac{p^2}{2m}e^{-\gamma t}+\frac{1}{2}m\omega^2e^{\gamma t}x^2,~(\gamma>0)\tag{1}$$ when promoted to quantum version, remains ...
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1answer
66 views

Does Noether's Theorem Apply in Galley's Extension to Lagrangian Mechanics?

I've been trying to digest The Classical Mechanics of Non-conservative Systems by Chad Galley. It describes an approach to applying Lagrangian mechanics to non-conservative systems via variable ...
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1answer
40 views

Why are simple models of coupled pendulums incapable of describing irreversible energy dissipation?

Consider two pendulums $A$ and $B$ coupled by a spring and also regard $A+B$ to be a completely isolated system. Let us start the system in an initial configuration where only one of the pendulums (...
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359 views

How do Hamilton's equations deal with non-conservative forces?

I have searched everywhere I know to look but I cannot find out how Hamilton's equations deal with non-conservative forces. In my understanding, Lagrangian mechanics deals with this as follows: the ...
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2answers
249 views

How can I express velocity as a function of position in a damped oscillation? [closed]

In a damped oscillation that obeys $x(t)=Ae^{-bt/2m}\cos(ωt)$ which shows the position of the oscillating object as a function of time, how can I express the velocity of the oscillating object as a ...
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1answer
70 views

What is the formula for how far a sound can be heard (taking into account dissipation)?

I was trying to figure out how far can a sound of 103 dB can be heard, so I converted it in W/m$^2$ (it gave me about $0.0200$ W/m$^2$) and then I used the formula “$I=P/4\pi r^2$” to find the maximum ...
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1answer
42 views

Eternal looping water tap

If i have a container like this (filled full with water): and I unplugged the small tap, would the water pressure be big enough to blast the water to the right side of the container and cause an ...
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2answers
80 views

Heat dissipation of a Resistor

When I was studying current electricity I found out that the amount of heat dissipating across a resistor is equal to the potential energy lost by an electron. Now I thought that a resistor provides ...
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1answer
112 views

Why friction losses depend on velocity squared?

This is the reason that suction pipes of centrifugal pumps are most of the times much wider than the discharge pipes and that restriction of blood flow in arteries is always an alarming event. Does ...
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1answer
37 views

Long term solution for a driven harmonic oscillator

Let $F(t)= \cos (\omega_d t) $ be the driving force of a harmonic oscillator of mass $m$ which is damped with a damping constant $b$ such that $F= -bv $ is the damping force and the spring exerts a ...
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1answer
135 views

Kubo formula to compute the energy dissipated in heat bath

In the case of a perturbed Hamiltonian $H_0$ \begin{equation} H=H_0 +\theta(t-t_0)W(t) \end{equation} at $t=t_0$ the Hamiltonian admits eigenvalues $E_n(t_0)$ and for positive $t-t_0$ then the ...
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2answers
45 views

Damped harmonic oscillation (LC circuit)

The $LC$ circuit I'm considering contains a capacitor, an inductor and an electrical resistance. There is no battery: intially the capacitor has a charge $Q$ and the electric current in the circuit is ...
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3answers
60 views

I want to know how law of conservation of energy holds in the generation of electricity in dams? [closed]

Basically law of conservation states that input energy is equal to the output energy. But i was wondering that in case of generating electricity in dams no input energy is required. As the dam only ...

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