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3
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2answers
248 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?
4
votes
2answers
6k views

What's a good textbook to learn about waves and oscillations?

I'm taking a course on waves and oscillations using Crawford from the Berkeley series (out of print excluding international copies), and would like to know if anyone has any suggestions for a better ...
8
votes
3answers
15k views

Does the human body have a resonant frequency? If so, how strong is it?

Inspired by this question on Music beta SE, I'm wondering if the human body has a strong resonant frequency. I guess the fact that it's largely a bag of jelly would add a lot of damping to the system, ...
5
votes
1answer
434 views

How do you define the resonance frequency of a forced damped oscillator?

Consider a forced, damped harmonic oscillator $$\ddot{\phi} + 2\beta \dot{\phi} + \omega_0^2 \phi = j(t) \, .$$ If I pick a sinusoidal driving force $j(t) = A \cos(\Omega t)$, I find $$\phi(t) = ...
17
votes
8answers
3k views

Why are sine/cosine always used to describe oscillations?

What I am really asking is are there other functions that, like $\sin()$ and $\cos()$ are bounded from above and below, and periodic? If there are, why are they never used to describe oscillations in ...
8
votes
1answer
242 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 + ...
3
votes
2answers
9k 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
vote
3answers
2k 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
votes
1answer
122 views

Neutrino mass and energy question

If a neutrino has mass then it travels less than the speed of light. Suppose I boost myself to the rest frame; i.e. bring it to rest in the laboratory. Now if it oscillates between different states ...
1
vote
2answers
303 views

Period of a simple pendulum accounting for friction

The period of a simple pendulum is $$T=2\pi\sqrt{\ell/g},$$ but no where in there do I see that it accounts for friction. Does it somehow account for friction, and if not, how could you do that?
2
votes
3answers
406 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..
1
vote
1answer
562 views

Meaning of “Simple” in Simple Pendulum and Simple Harmonic Motion?

I have gone through the Phys.SE question Why is simple harmonic motion called so?. From the 1st answer of this Question it seems to me that another type of "Harmonic motion" is "Damped Harmonic ...
1
vote
2answers
747 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 ...
1
vote
0answers
167 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 ...
6
votes
2answers
581 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = ...
10
votes
3answers
2k views

What is the period of a physical pendulum without using small-angle approximation?

What is the expression for the period of a physical pendulum without the $\sin\theta\approx\theta$ approximation? i.e. a pendulum described by this equation: $$ mgd\sin(\theta)=-I\ddot\theta $$ ...
4
votes
1answer
81 views

Neutrino flavor eigenstate interaction with matter

We know that neutrino eigenstates are not mass eigenstate and this therefore produces neutrino oscillations. This is, however, deduced from the fact that the neutrino of one flavor produces the ...
4
votes
3answers
340 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? ...
3
votes
3answers
151 views

What is the time period of an oscillator with varying spring constant?

It is well known that the time period of a harmonic oscillator when mass $m$ and spring constant $k$ are constant is $T=2\pi\sqrt{m/k}$. However, I would be interested to know what the time period ...
2
votes
1answer
594 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 ...
2
votes
1answer
1k 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
vote
2answers
424 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\; ...
11
votes
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 ...
3
votes
1answer
380 views

The universality of the Stuart-Landau equation to describe nonlinear oscillators

I have read numerous papers which boldly suggest that the Stuart-Landau equation can be successfully used to model any weakly nonlinear oscillating system near a Hopf bifurcation. Even thought it has ...
1
vote
1answer
2k views

Does damping force affect period of oscillation?

In my physics notes, it has been given that the damping force increases the period of oscillation. I am unable to understand this part. How is this possible? The only relation I know is that as the ...
1
vote
2answers
2k views

Can a simple pendulum be considered a simple harmonic oscillator?

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

In an RLC series circuit on resonance, how can the voltages over the capacitor and the inductor be larger than the source voltage?

Consider an RLC circuit in series, of the form If the source drives the circuit in AC at the resonance frequency $\omega =1/\sqrt{LC}$, the peak-to-peak voltages on the capacitor and the inductor, ...
0
votes
1answer
952 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 ...