# Questions tagged [oscillators]

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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 does my ID card oscillate sideways when walking?

When I was going to my school with my ID card hanging around my neck, it started doing oscillations like a pendulum. I was moving forward and it was oscillating left to right and right to left. What ...
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### Why does a simple pendulum or a spring-mass system show simple harmonic motion only for small amplitudes?

I've been taught that in a simple pendulum, for small $x$, $\sin x \approx x$. We then derive the formula for the time period of the pendulum. But I still don't understand the Physics behind it. Also, ...
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### What is a mode?

The word mode pops up in many fields of physics, yet I can't remember ever encountering a simple but precise definition. After having searched fruitlessly on this site as well, I feel that even ...
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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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### Non-resonant but efficient frequencies

I understand that if the frequency of a driving force coincides with the natural frequency of an oscillator (say a pendulum), the rate at which energy is transferred to the same is maximized. However, ...
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### 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 ...
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### Definition of the $Q$ factor?

According to Wikipedia, the $Q$ factor is defined as: $$Q=2\pi\frac{\mathrm{energy \, \, stored}}{\mathrm{energy \, \,dissipated \, \, per \, \, cycle}}.$$ Here are my questions: Does the energy ...
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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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### 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, ...
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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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### Why is the wave equation so pervasive?

The homogenous wave equation can be expressed in covariant form as $$\Box^2 \varphi = 0$$ where $\Box^2$ is the D'Alembert operator and $\varphi$ is some physical field. The acoustic wave ...
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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 is the oscillation frequency of a buoyant cylinder?

Suppose a cylinder sits upright in "dry water" (zero viscosity). The cylinder has half the density of the water, and we'll ignore the dynamics of the atmosphere. If I push the cylinder down some past ...
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### A damped harmonic oscillator is NOT a dissipative system?

I know this sounds rather insane, but it says so in my book. The argument is the following: Given a damped harmonic oscilator $$\ddot{q}+\frac{b}{m}\dot{q}+\frac{k}{m}q=0 \tag1$$ this system can be ...
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### Will a violin string keep vibrating for a longer time in vacuum than in air?

Hitting a string of a violin or a guitar will cause that string to vibrate, but after short time the amplitude of the vibration will decay, consequently the produced sound will die out. I suppose ...
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### Can we guess the periodic/aperiodic nature of motion from the equation of motion?

The equation of motion of a pendulum with a bob of mass $m$, and hanging by means of a massless thread of length $T$ is given by $$\ddot{\theta}+\frac{g}{l}\sin\theta=0,$$ and that of a damped one-...
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### Resonance peak broadening due to losses: physical reason

I wonder why when losses are present in a oscillator, the width of the resonance peak is broadened. More precisely: why, when losses are present, can the amplitude reach nearly the maximal one (the ...
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### Springs with some finite mass

Let us consider a spring which is having some finite mass. By the help of some external agent the spring has been extended by some distance $x$. Will the restoring force produced in the spring still ...
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### 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? $$m\dfrac{d^2x}{dt^2}=F=-\dfrac{dU}{dx}=-3kx|x|.$$ ...
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### Correct way of solving the equation for simple harmonic motion

I am considering the equation for simple harmonic motion, which is $\ddot x +\omega ^2x=0$ To solve this, I have seen three approaches. This is confusing as I do not know which approach is physically ...
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### Why does the acceleration $g$ due to gravity not affect the period of a vertically mounted spring?

For a vertically mounted spring, I was looking at the formula $T= 2\pi \sqrt{m/k}$ for a period. Why doesn't the gravitational acceleration $g$ factor in?
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### How can a pendulum have amplitude greater than $\pi$?

How can a pendulum have amplitude angle greater than $\pi$? I've been reading about phase plots, which are graphs of the $\frac{d\theta}{dt}$ on the $y$ axis and $\theta$ on the $x$ axis, shown below. ...
516 views

### Are there any fully analytically solvable nonlinear oscillators?

I'm trying to find a simple one-dimensional problem, in which a particle would oscillate with some energy, and the period of oscillation would depend on particle energy (unlike in harmonic oscillator)....