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Questions tagged [oscillators]

A mechanical or electronic system or device that works on the principles of oscillation, that is a periodic fluctuation between two things based on changes in energy. These range from abstract models such as a harmonic oscillator to electrical devices such as an LC circuit.

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How Does Frequency Change With Damping (Underdamped Harmonic Oscillators) [closed]

I'm studying harmonic oscillators and I'm trying to model a system where both the frequency and amplitude decay over time. This is throwing me off because frequency decay is much less intuitive than ...
Jeremy Kievit's user avatar
35 votes
5 answers
5k views

Why does the pet's water bowl overflow?

So when i give the pet fresh water in a stainless steel bowl that i place on a mat according to the attached picture, from $t=0$ the bowl is at rest, the water normally oscillates in the bowl like a ...
user721108's user avatar
0 votes
2 answers
194 views

Do lasers with optical isolator or synchrotron radiation sources allow for Rabi cycles?

In Rabi cycle two-level system cyclically transitions between ground and excited state - bringing question where their energy difference goes during these transitions? For transition from ground to ...
Jarek Duda's user avatar
0 votes
1 answer
30 views

If I have a simple pendulum performing oscillations, whose string is snapped when it is at an extreme position, what will happen?

If I have a simple pendulum performing oscillations, whose string is snapped when it is at an extreme position, will it immediately fall vertically downwards because of gravity or will it continue ...
SuperSexyTrash's user avatar
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1 answer
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"Friction at a contact point", rubber-band experiment

I was working on some practice problems in my book, and the question was to describe all the energy conversions that happens when a person pulls on a rubber band and hits it on a board (any type of ...
SMK's user avatar
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1 answer
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Would a nearby electron be attracted/repulsed due to the oscillating $\vec E$ and $\vec B$ field of a passing electromagnetic wave? [closed]

I had just read up on the propagating electromagnetic wave equation, and realized that I do not know how to apply it in practice beyond knowing the equation... Suppose $$\vec E (x, t) = \begin{bmatrix}...
James's user avatar
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1 answer
36 views

Spherical pendulum newtonian [closed]

I want to solve the equation of motion of mass $m$ in a Newtonian way. I don't know what kind of force makes $φ$ directional motion. In addition, if I solve this problem with Newton's equation of ...
SungJin Park's user avatar
0 votes
1 answer
57 views

If friction is not proportional to velocity, why do we model it as such when considering damped oscillations? [duplicate]

Early in our study of mechanics, we learn that friction is usually proportional only to normal force, without dependence on velocity. However, during our studies of damped oscillations, we often model ...
Dominic Stewart-Guido's user avatar
1 vote
1 answer
43 views

Kinematics and dynamics of a ballistic pendulum

In which Physics textbooks can one find comprehensive content on the kinematics and dynamics of a ballistic pendulum both in the approximation of the mass and a distributed mass with uniform density?
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2 answers
63 views

Extending the Lagrangian of a double pendulum to systems with more complex shapes

The total kinetic energy of a double pendulum can be calculated as follows: $$L = \frac{1}{2} (m_1 + m_2) {l_1}^2 \dot{\theta_1}^2 + \frac{1}{2} m_2 {l_2}^2 \dot{\theta_2}^2 + m_2 l_1 l_2 \dot{\...
Riccardo Zanardi 's user avatar
1 vote
1 answer
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Foucault pendulum with General Relativity

It is well-known that the plane of the swing of a Foucault pendulum exhibits parallel transport (wrt to the Levi-Civita connection) of a round sphere. Seeing as Einstein's relativity theories ...
Integral fan's user avatar
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1 answer
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Spherical quantum oscillator: Is energy smaller than the potential?

A particle with mass $m$ is inside the spherical quantum well $V(r)$: \begin{equation} V(r)= \begin{cases} -V_0, & \text{if}\ r<a \\ 0, & \text{otherwise} \end{cases} \...
haifisch123's user avatar
0 votes
1 answer
18 views

How do you convert the damping coefficient to speed dependent drag coefficient (for low speeds)?

I'm trying to understand how to convert the damping coefficent to the speed dependent drag coefficient for an investigation I am doing for school.
Gayathri Ghosh's user avatar
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3 answers
60 views

Investigation Results of Damping of A Spring Showing Changing Phase Angle? Why?

In an experiment I've recorded the displacement of the spring over time, investigating underdamped simple harmonic motion. Using pre-existing formulae the data should conform to a curve of the form $$...
Eshwar Kolli's user avatar
6 votes
3 answers
998 views

How does a guitar string produce sound?

I'm curious about the mechanism of a guitar producing sound. Of course, I know once a string is plucked it vibrates in a superposition of several harmonics, but what I don't know is what happens next. ...
Lagrangiano's user avatar
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2 answers
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Rescaling time in differential equations

On a scientific paper, I found the following equations about a compass gait (one leg behaves like an inverted pendulum, the other one as a simple pendulum; $\theta$ and $\phi$ are time-dependent): $$ \...
Federica Guidotti's user avatar
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0 answers
80 views

What are standing waves?

What are standing waves? I'm new to wave mechanics and I don't seem to be able to understand why standing waves form. My specific doubt is how do they form and why do they form? Some intuition might ...
BlackKnight23's user avatar
1 vote
3 answers
138 views

Why we take only the real part of a solution as the actual motion?

I am taking Analytical Mechanics, and in Goldstein's book, chapter 6 (page 241) about linear oscillations, he says the following: "... $\eta_i=Ca_ie^{-i\omega t}$ (6.11) ... It is understood of ...
A24601's user avatar
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3 votes
4 answers
196 views

Does entanglement rule out oscillating properties?

This will be a very noob question and I am a novice but I just wanted to understand entanglement better. This is just a toy analogy that I thought of and again, I don’t know the intricate details of ...
user avatar
-1 votes
2 answers
79 views

How can maximum kinetic energy not equal to total energy in SHM$?$ [closed]

A linear harmonic oscillator of force constant $2×10^6$$ \,\text{N}\,\text{m}^{-1}$ and amplitude $0.01 \,\text{m}$ has a total mechanical energy of $160 \,\text{J}$. Find ratio of maximum potential ...
MathStackexchangeIsMarvellous's user avatar
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1 answer
36 views

How to decide for correct value of phase difference?

A sinusoidal wave is propagating along a stretched string that lies along x-axis. The wave is moving in +x-direction. Figure shows the graph of transverse displacement of particles of the string at x =...
Garv Chaudha's user avatar
2 votes
1 answer
143 views

Are vibrating strings in string theory perpetual motion?

I have never learned string theory, so please forgive me if my question sounds naive or obvious, but I would like to know and I am most likely wrong. As far as I know, strings vibrate in different ...
Tachyon's user avatar
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1 answer
43 views

Shaking pencil's hyperbola formula? [closed]

When you typically shake a pencil, it bends and forms a curve (hyperbola?). I want to formalize this phenomenon, but I'm not sure how to do it. I'd like to incorporate factors such as amplitude, ...
Myeongjun Chae's user avatar
0 votes
3 answers
82 views

Derivation of Differential Equation of a Simple Pendulum [closed]

This pretty much a simple question and i seem to be making a dumb error here, but nonetheless I can't get the correct answer for the general equation of a pendulum which is :$$\ddot\theta=-\frac{g}{L}...
Star Gazer's user avatar
0 votes
0 answers
32 views

Frequency of Pendulum Outside the Small Angle Approximation [duplicate]

I understand that if one makes the small angle approximation, the angular frequency of, say, a pendulum, is easy to find as $\sqrt{k/m}$. Without making any approximations and sticking with the ...
user67637's user avatar
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2 votes
3 answers
125 views

Foucault's own explanation of his pendulum

Foucault never gave a detailed explanation of why the period of the turning of his pendulum depended on the sine of the latitude, but he wrote a letter saying as follows: "I begin by boldly ...
Dirac's user avatar
  • 21
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0 answers
19 views

Perturbative analysis of pendulum via virial theorem

I am following Sivardiere, Jean. "Using the virial theorem." American Journal of Physics 54.12 (1986): 1100-1103. The pendulum with length $L$ has equation of motion $\ddot{x}=-\omega_0^2 \...
MaudPieTheRocktorate's user avatar
14 votes
8 answers
4k views

Can motion be oscillatory but not periodic?

The equation of motion of a particle is $x = A \, \mathrm{cos}\left[(\alpha t)^2\right]$. What type of motion is it? The answer to this question in my textbook was: "Oscillatory but not periodic&...
Haider's user avatar
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3 answers
65 views

Oscillating inverted hemisphere Lagrangian mechanics problem

I am trying to solve a hw problem on Lagrangian mechanics. Here is the problem: The main issue I am having is setting up the kinetic energy. I don't understand whether the hemisphere has both ...
mathlover123's user avatar
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0 answers
15 views

Molecular stretching oscillations directions

Molecular stretching oscillations directions. If we say that vertical oscillation is up/down. Then, left/right and front/back are horizontal oscillations. Hence, when we measure oscillations of ...
Niss Green's user avatar
0 votes
0 answers
58 views

References describing how the initial angular displacement of a pendulum affects its damping ratio?

I'm writing a research paper exploring how damping ratio of a simple pendulum relates on its initial angular displacement. In order to validate the findings of my paper, I am required to include a ...
0 votes
0 answers
13 views

Movement of a mass on a spring in damped SHM

Suppose a ball is connected to a spring attached to a wall, and they are in space, i.e. assume no gravity. The ball is put into a fluid with Stoke's drag and oscillates backwards and forwards relative ...
Yitian Chen's user avatar
0 votes
0 answers
74 views

How does time period change with damping in oscillations?

Does time period increase or decrease with an increase in damping? I've had contradicting answers. My teacher has told me that time period increases with damping. It does make sense in a way because ...
Devil's Advocate 2321's user avatar
1 vote
1 answer
34 views

Different Shape for Fliptime Fractal

This is related to my previous question. I am generating images of how long it takes for a double pendulum to flip in different configurations. I was trying to find the shape of where it isn't ...
MaximeJaccon's user avatar
2 votes
1 answer
51 views

How to demonstrate in a simple way that this system of differential equations form a damped harmonic oscillator? [closed]

How may I demonstrate in the most simple way that the following system of differential equation form a damped harmonic oscillator ? $$ \dot x = -\alpha_x x - \omega y \\ \dot y = -\alpha_y y + \omega ...
chmike's user avatar
  • 123
1 vote
0 answers
41 views

What is the name of this pendulum? [closed]

What is the name of a pendulum with two parallel string hung vertical to a rod, and giving the rod an initial force would make it swing left and right, doing simple harmonic motion? What is the ...
user398341's user avatar
2 votes
1 answer
80 views

Double Pendulum Cannot Flip

This source, The Double Pendulum Fractal provides an image of a flip-time fractal for the rods of a double pendulum. The authors state that it is "not energetically possible for either pendulum ...
MaximeJaccon's user avatar
0 votes
1 answer
37 views

Is there a class of phenomena the description of which is not limited to the study of the properties of individual harmonic waves?

There are lots of examples of oscillatory phenomena in nature the description of which boils down to simple harmonic behavior, i.e. to Cosine/Sine/Complex Exp. This answer explains that we use sines ...
shamil khal's user avatar
2 votes
0 answers
34 views

The interpretation of the Bose occupation factor

I was reading into the Oxford solid state basics, by Steven H.Simon and I stumbled upon a confusing interpretation of the Bose Occupation factor: $$n_B (x) = \frac{1}{e^x-1}$$ with: $$x = \beta \hbar \...
SAMS's user avatar
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2 votes
1 answer
46 views

Plot of Number of Oscillations of a Pendulum

I have been studying the oscillations of a ball attached to a string which is released from some initial angle $\theta$. The number of complete oscillations over a certain time interval $\Delta t$ is ...
Tom's user avatar
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0 votes
1 answer
43 views

What is the equation if that projection starts SHM on the $x$-axis from extreme position?

Consider A particle performing Uniform Circular Motion. We know that its projection on diameter performs SHM. Then, if that projection starts SHM on the y axis from mean position, then $y=A\text{sin}(...
NERD's user avatar
  • 11
5 votes
3 answers
2k views

Where does the negative sign disappear?

The defining equation for simple harmonic motion is such $$a=-ω^2x$$ When we find the centripetal acceleration of an object in orbit we use the formula $$a=ω^2r$$ As a consequence of the accleration ...
Quin Gardiner Bax's user avatar
0 votes
0 answers
48 views

Question about a harmonic oscillator

I was solving the following problem on harmonic oscillation and I don't understand a specific part in the proof. I will emphasize (italic) the part which I don't understand. Problem: The following ...
Darius Chitu's user avatar
0 votes
0 answers
15 views

Rotating disc with viscous damping with large initial angle (always 90 degrees) (unbalance/instability)

I have an application for a rotating disc with inertia that is put on a "knife edge" balancing fixture. The disc is then released in order to find the "heavy spot", once identified ...
Mikro1234's user avatar
2 votes
0 answers
45 views

Finding condition for Adiabaticity

I have a differential equation describing a resonator that looks like this: $$ \frac{d\alpha(t)}{dt} = [j a - b]\alpha(t) + \sqrt b e^{jct}$$ where I can solve it putting: $$\alpha(t) = \alpha e^{jct}$...
SiPh's user avatar
  • 21
0 votes
0 answers
86 views

Skating off an edge with torque ambiguity

Problem In this particular case of a dynamic skating motion combining translation and rotation, I consider the question of determining the appropriate torques and applying the correct rotational ...
Jens's user avatar
  • 1,302
2 votes
0 answers
50 views

Example of spring system modelled by $\ddot{x} + F(x,\dot{x}) \dot{x} + x = 0$, with given conditions on $F$

Consider the oscillator equation $$\ddot{x} + F(x,\dot{x}) \dot{x} + x = 0$$ where $F(x,\dot{x}) < 0$ if $r \leq a$ and $F(x,\dot{x}) > 0$ if $r \geq b$, where $r^2 = x^2 + \dot{x}^2$. What ...
Leonidas's user avatar
  • 121
2 votes
6 answers
108 views

Is time period of a pendulum in an accelerating elevator dependent on the weight of the bob?

If a simple pendulum is in an elevator accelerating upwards, Its $T$ decreases. But why is that? The only thing that changes is the apparent weight so does $T$ depend on the weight of the bob but ...
Spluesh's user avatar
  • 61
0 votes
0 answers
110 views

Lyapunov Exponent for Double Pendulum

I want to calculate the Lyapunov Exponent for a double pendulum, with a small change in the initial angle. In this study, the authors used the formula $\frac{1}{t}{ln(\frac{d}{d_0})}$ as $t$ tends to ...
MaximeJaccon's user avatar
0 votes
1 answer
22 views

EOM Double Pendulum with Mass of Rods

All the equation's of motion for a double pendulum do not include the masses of both rods. Is there an EOM for a double pendulum that takes into account the masses of the rods (not just the bobs)? Or, ...
MaximeJaccon's user avatar

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