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2answers
133 views

Linearized equations

What is $V_{\alpha\beta}$? And what is a symmetric, positive definite potential energy matrix? And why is there a linearized equation like this?
6
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1answer
133 views

Caldeira-Leggett Dissipation: frequency shift due to bath coupling

I am trying to understand the Caldeira-Leggett model. It considers the Lagrangian $$L = \frac{1}{2} \left(\dot{Q}^2 - \left(\Omega^2-\Delta \Omega^2\right)Q^2\right) - Q \sum_{i} f_iq_i + ...
1
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3answers
858 views

Frequency of small oscillation of particle under gravity constrained to move in curve $y=ax^4$

How to find the frequency of small oscillation of a particle under gravity that moves along curve $y = a x^4$ where $y$ is vertical height and $(a>0)$ is constant? I tried comparing $V(x) = \frac ...
2
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3answers
224 views

Condition for closed orbit [closed]

I'd like to know when an orbit is closed. I know that, to have a closed orbit, there is a ratio that must be a rational number, but I don't know other things..
2
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2answers
4k views

Phase difference of driving frequency and oscillating frequency

If a mass is attached to a spring and is oscillating (SHM). If a driving force is applied it must be at the same frequency as the mass's oscillation frequency. However I'm told that the phase ...
1
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2answers
460 views

How could this damped oscillator ever go to infinity? Or negative infinity for that matter?

This is an ODE problem,but I cannot visualize why it can go to infinity or negative infinity. Consider $$x'' -6x' + 8x = 0$$ Where $x''$ is acceleration, $-6x'$ is the ...
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0answers
156 views

Conveyor scales modeling

Assume we have a conveyor scales. Which consists of scales, and motor with conveyor belt placed above, so that the boxes can be measured (weight) while moving above. What I want is to create the model ...
11
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1answer
2k views

Does a guitar sound different in zero (or micro) gravity?

Seeing a video of astronaut Chris Hadfield playing a guitar on the International Space Station made me wonder if a guitar or other stringed instrument played in zero-G would sound any different than ...
4
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3answers
237 views

Non-SHM oscillatory motion

How to solve these kind of questions , where $|F| \propto x^2$? How to find time period and velocity type related things to the oscillatory motion? ...
2
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1answer
527 views

What is the amplitude of the limit cycle of the van der Pol oscillator?

In the second edition of Classical dynamics of particles and systems by Jerry B. Marion, it is said that the van der Pol equation $$\ddot{x}-\mu\left({x_0}^2-x^2\right)\dot{x}+{\omega_0}^2x=0$$ where ...
1
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2answers
253 views

Oscillation with exponentially increasing period

I am trying to build a model for a certain type of oscillatory behaviour with a kind of exponential dilatation. How can I modify the function of a simple cosine oscillation $\psi(x)=A_0 \cos(2\pi\; ...
1
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1answer
141 views

Why maximum energy transfer at natural frequency even if max amplitude occurs below $f_0$

This is a paragraph from my book: "For a damped system, the resonant frequency at which the amplitude is a maximum is lower than the natural frequency.However, maximum transfer of energy, or energy ...
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2answers
611 views

Why is simple harmonic motion called so?

Is the motion of a simple pendulum, a simple harmonic motion? It stops vibrating after sometime.
0
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1answer
445 views

What makes up a resonator of radio?

I was reading this article about resonators. Quote: The sine wave that matches that particular frequency will get amplified by the resonator, and all of the other frequencies will be ...