# Tagged Questions

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### Why are the harmonics of a piano tone not multiples of the base frequency?

I was trying to figure out which piano keys were being played in an audio recording using spectral analysis, and I noticed that the harmonics are not integer multiple of the base note. What is the ...
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### Why aren't the lengths of the bars on a toy glockenspiel proportional to the wavelengths?

As you might already know, frequency of musical notes is arranged in a such a way that if, for example, an A note has frequency of $x$, another A note which is placed one octave higher would produce ...
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### 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 ...
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### Why doesn't a tied balloon behave like a pendulum?

It is well known that a tied weight will oscilate under the effect of gravity if left from aside, like a pendulum. However, if we tie a helium balloon to the ground from and left it form the floor (...
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### Rope waves with a twist

In the picture you see a person walking a slackline. A slackline is a tensioned flatband of polyester. Typical tensions are between 1 kN to 15 kN depending on the length of the line. The lines are ...
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### What creates the chaotic motion on a double pendulum?

As we know, The double pendulum has a chaotic motion. But, why is this? I mean, the mass of the two pendulums are the same and they have the same length. But, what makes its motion random? I'm just ...
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### What is a full cycle in damped oscillation?

Maybe it seems a dumb question, but I can't understand what the cycle in a damped oscillation is? Let's take an example: In harmonic motion, one cycle is the smallest distinguishable part of wave ...
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### Is it possible to find a “replacement pendulum” for a system of two equal but perpendicular pendulums?

I ask this question, because at the end of this long day I'm just too dazed to derive the proofs myself (even though I know that I should feel ashamed for this). So, the question: Given two ...
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In the approximation $$-(g/ \ell) \sin \theta \approx -(g/ \ell) \theta$$ we make an error $R$ which is $O(\theta ^3)$. If i did well my calculations it is estimated by $$R\leq|(g / \ell)(\theta^3/3!)... 0answers 82 views ### Why are vibrations so common? [closed] Why are vibrations so common? We all know, or pretend to know, that symmetries and the least action principle lead to conservation laws.Is there something more fundamental behind the fact that ... 3answers 361 views ### Non-SHM oscillatory motion How to solve these kind of questions , where |F| \propto x^2? How to find time period and velocity type related things to the oscillatory motion?$$m\dfrac{d^2x}{dt^2}=F=-\dfrac{dU}{dx}=-3kx|x|.$$... 2answers 7k views ### What's a good textbook to learn about waves and oscillations? I'm taking a course on waves and oscillations using Crawford from the Berkeley series (out of print excluding international copies), and would like to know if anyone has any suggestions for a better ... 2answers 839 views ### Reflected and refracted light have same frequency as that of the incident light frequency. Why? My text book says- When a monochromatic light is incident on a surface separating two media, the refracted and reflected light both have the same frequency as the incident frequency. Can anyone ... 3answers 202 views ### What is the time period of an oscillator with varying spring constant? It is well known that the time period of a harmonic oscillator when mass m and spring constant k are constant is T=2\pi\sqrt{m/k}. However, I would be interested to know what the time period ... 2answers 175 views ### Neutrino mass and energy question If a neutrino has mass then it travels less than the speed of light. Suppose I boost myself to the rest frame; i.e. bring it to rest in the laboratory. Now if it oscillates between different states ... 2answers 355 views ### Synchronization phenomenon: A simple explanation? Being from a mathematical background, physicists' intuitive arguments always seemed challenging for me to follow. I am currently reading a book called "Synchronization: A Universal Concept in ... 3answers 166 views ### What is the meaning of U''(x)=0? Most potentials with a minimum can be described approximately as a harmonic oscillator. So the procedure is to Taylor expand U(x):$$U(x)=U(0)+U'(0)x+\frac{1}{2}U''(0)x^2 +...$$If we suppose ... 2answers 236 views ### Definition of quantum anharmonicity I have been reading research papers in mathematical physics for some months now, and I've seen the the term "anharmonic oscillator" quite frequently. At first I assumed that given a Schrodinger ... 1answer 90 views ### Neutrino flavor eigenstate interaction with matter We know that neutrino eigenstates are not mass eigenstate and this therefore produces neutrino oscillations. This is, however, deduced from the fact that the neutrino of one flavor produces the ... 0answers 222 views ### Relation of the Bloch-Siegert shift to the rotating pot lid I see in Wikipedia that the Bloch-Siegert shift is analogies to the rotating pot lid, could you explain that analogy? The Bloch-Siegert shift is a phenomenon in quantum physics that becomes ... 2answers 12k views ### Phase difference of driving frequency and oscillating frequency If a mass is attached to a spring and is oscillating (SHM). If a driving force is applied it must be at the same frequency as the mass's oscillation frequency. However I'm told that the phase ... 3answers 135 views ### How can F_0\cos\omega t change to F_0e^{i\omega t} in driven oscillator equation? I have one thing that confuses me on deriving the solution for the Linear Forced Oscillator. Suppose we have the equation as$$ma + rv + kx = F_0 \cos \omega t$$What confuses me is when the driving ... 2answers 272 views ### Linearized equations What is V_{\alpha\beta}? And what is a symmetric, positive definite potential energy matrix? And why is there a linearized equation like this? 1answer 76 views ### Why is energy in a system typically able to be described using quadratic expressions? This might be more of an applied math question. Why is the energy of a system typically able to be described using quadratic expressions. Is there an underlying mechanic that drives this? 1answer 170 views ### What is the physical interpretation of the linear coefficient in this ODE for projectile motion? For the second order ODE governing the position of a projectile subject to air resistance$$ m\frac{d^2x}{dt^2} +k\frac{dx}{dt}+mg=0 \quad k>0, \> x(0)=0, \> x'(0)=V>0 $$a non-... 1answer 215 views ### Why don't we use quater-circular dees instead of semi-circular dees in a Cyclotron This is the setup, I have in my mind: O1, O2, O3 and O4 are 4 oscillators. The arrows in between the Dees represent the alternating EMF the Oscillators will generate. I think we can easily adjust ... 2answers 517 views ### Probability of position in linear shm? The problem that got me thinking goes like this:- Find dp/dx where p is the probability of finding a body at a random instant of time undergoing linear shm according to x=a\sin(\omega t). ... 2answers 230 views ### “Inverted” quantum oscillator I'm trying to understand the problem of the "inverted" oscillator, which has the following Hamiltonian:$$ \hat{H}=\frac{\hat{p}^{2}}{2m}-\frac{k\hat{x}^{2}}{2} $$Suppose that a particle at the ... 1answer 271 views ### How does resonance store vibrational energy? In the wiki article, it is written that in resonance, maximum amplitude is possible as vibrational energy is stored. What does that statement mean? How is energy stored so that max. amplitude occurs?... 1answer 789 views ### Simple pendulum period in three different cases Imagine you have a simple pendulum hanging on the ceiling of a train which has a period called T. How will the period be in the following cases: When the train is in circular motion in a curve of ... 1answer 772 views ### Numerical computation of the Rayleigh-Lamb curves The Rayleigh-Lamb equations:$$\frac{\tan (pd)}{\tan (qd)}=-\left[\frac{4k^2pq}{\left(k^2-q^2\right)^2}\right]^{\pm 1} (two equations, one with the +1 exponent and the other with the -1 exponent) ...
I was taught at school that the formula for period of a pendulum is $T=2\pi \sqrt{\frac{l}{g}}$ Later I found out that this is only an approximation valid for small angles and the accuracy of this ...