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 ...
2k views

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 ...
9k views

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 ...
45k 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, ...
4k views

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 (...
442 views

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 ...
384 views

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-...
735 views

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 ...
1k views

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 ...
681 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? $$m\dfrac{d^2x}{dt^2}=F=-\dfrac{dU}{dx}=-3kx|x|.$$ ...
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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)....