Questions tagged [oscillators]

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56
votes
2answers
4k views

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 ...
39
votes
3answers
4k views

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 ...
26
votes
3answers
5k views

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, ...
23
votes
3answers
12k views

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 ...
21
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8answers
9k 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 ...
20
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3answers
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, ...
16
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3answers
17k 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 ...
16
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3answers
9k views

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 ...
15
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3answers
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 ...
15
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3answers
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, ...
13
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4answers
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 (...
13
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1answer
445 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 ...
13
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2answers
388 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 ...
13
votes
2answers
1k views

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 ...
12
votes
2answers
969 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: $$S=\...
11
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1answer
3k 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 ...
11
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3answers
4k 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: $$ mgd\sin(\theta)=-I\ddot\theta $$ ...
10
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5answers
2k views

How can I prove that a state of equilibrium is unstable?

In the particular problem I encountered, an electric field was zero at the origin and we were meant to prove that a particle at the origin was in an unstable state of equilibrium. Is it enough to ...
10
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2answers
2k views

How can you make harmonics on a string? [duplicate]

For an oscillating string that is clamped at both ends (I am thinking of a guitar string specifically) there will be a standing wave with specific nodes and anti-nodes at defined $x$ positions. I ...
10
votes
5answers
1k views

A conceptual doubt regarding Forced Oscillations and Resonance

While studying about the Resonance and Forced Oscillations, I came across a graph in my textbook that is given below:- Now, the author writes As the amount of damping increases, the peak shifts ...
10
votes
2answers
1k views

Quantum shot-noise and the fluctuation dissipation theorem

Classically, shot noise observed in the signal generated by a laser incident on a photodiode is explained as being due to the quantization of light into photons, giving rise to a Poisson process. In ...
10
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2answers
3k views

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

Consider a forced, damped harmonic oscillator $$\ddot{\phi} + 2\beta \dot{\phi} + \omega_0^2 \phi = j(t) \, .\tag{1}$$ If I pick a sinusoidal driving force $j(t) = A \cos(\Omega t)$, I find $$\phi(...
10
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1answer
313 views

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 ...
10
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3answers
2k views

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 ...
9
votes
1answer
376 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 + \sum_{i}\...
8
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6answers
2k views

Simple Pendulum Why Generalized Coordinate Always Angle?

When writing the equations of motion for the simple pendulum, why do textbooks always choose $\theta$ to be the generalized coordinate? The force of gravity is in the y-direction so wouldn't it be ...
8
votes
4answers
28k views

Phase difference of driving frequency and oscillating frequency

Suppose 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' oscillation frequency. However I'm told that the phase ...
8
votes
3answers
2k views

What is the qualitative cause for a driven oscillator to have a max. amplitude during resonance?

The steady-state motion of a driven oscillator is given by;$$x =\underset{\text{amplitude}} {\dfrac{F_0}{m({\omega_0}^2 - {\omega}^2)}} \cos\omega t.$$ As we see, the amplitude becomes maximum when $$\...
8
votes
3answers
540 views

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-...
8
votes
6answers
756 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 ...
7
votes
6answers
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 ...
7
votes
3answers
686 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? $$m\dfrac{d^2x}{dt^2}=F=-\dfrac{dU}{dx}=-3kx|x|.$$ ...
7
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4answers
5k views

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 ...
7
votes
6answers
19k views

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?
7
votes
3answers
315 views

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. ...
7
votes
2answers
517 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)....
7
votes
2answers
393 views

How much upward force due to ground vibrations does the Earth exert on you?

Say you're walking by the highway and you can feel the vibrations of cars moving along. How would you approximate the force that the ground is exerting on your feet due to these vibrations?
6
votes
2answers
813 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} = -...
6
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3answers
7k views

Why do objects have resonance at natural frequency?

What actually is a natural frequency for an object and what makes it vibrate with increased amplitude when coupled with an external oscillator that matches the natural frequency?
6
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1answer
111 views

Oscillation of Chocolate bar on soda [closed]

Why does a piece of chocolate bar oscillate in soda (i.e. floats then after a while sinks and vice versa)? What parameters does the period of oscillation rely on? Is there a specific formula that ...
6
votes
4answers
533 views

What prevents sound to be just wind?

I have two questions about the physics of sound. As a background, I know the process of sound production can be understood as 3 stages that happen continuously: An object oscillates back and forth ...
6
votes
1answer
16k views

How do I solve for the phase constant given the amplitude and the angular frequency?

A piston (with mass M) in a car engine is in vertical simple harmonic motion with amplitude A. The engine is running at a period T. Suppose a small piece of metal with mass m were to break loose ...
6
votes
2answers
647 views

Conservation of energy in a non-linear oscillator

I have a homework question about a "non-linear oscillator". I actually have an answer to this question, but the answer I get is stronger than what is needed according to the question. The question ...
6
votes
0answers
103 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 ...
5
votes
2answers
815 views

Pendulum period [duplicate]

In plane pendulum problem, we can calculate its period using elliptic integration. In SHO problem, we use approximation such that $\theta\ll 1$ and get the period, $2\pi\sqrt{l/g}$. Is there another ...
5
votes
3answers
839 views

Finding the period of an anharmonic oscillation by substituting the solution for SHM

I came across the problem below, and I am confused about the solution provided. The solution method is to substitute the result for SHM into an equation which is not harmonic, and rearrange to find ...
5
votes
2answers
112 views

Why are sinusoids so common in nature? [duplicate]

When we are introduced to waves in school, we are often presented with a picture of a sinusoid (or a cosinusoid). Sinusoids can represent the way many physics phenomena behave, still.... Why are ...
5
votes
4answers
7k 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 ...
5
votes
2answers
272 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 ...
5
votes
1answer
112 views

How can dissipative/friction terms be incorporated into a Lagrangian?

I'm trying to find a suitable Lagrangian for a damped harmonic oscillator, a system that satisfies the following equation of motion: $$m \ddot{x} + \gamma \dot{x} + \frac{d\phi}{dx} = 0.$$ What I ...