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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In the undriven $RLC$ circuit, why would one conjecture the solution with $Ae^{Zt}$ when we perfectly know that critical case has $te^{-\alpha t}$?
There's something I don't quite get in this video (MIT $8.02$ course titled "Electricity and Magnetism", video number $208$, taught by Pr. Peter Dourmashkin).
Professor conjectures the ...
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Conjecturing the homogeneous solution of a $2^{nd}$-order constant coefficients ODE - why conjecturing a $3$ D.O.F. solution in this course?
In this video (MIT $8.02$ course titled "Electricity and Magnetism", video number $208$, taught by Pr. Peter Dourmashkin) professor solves the undriven $RLC$ circuit ODE ($2^{nd}$-order ...
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What's the easiest way to get the speed at the tip of a double pendulum?
Say we have a double pendulum consisting of two rods of lengths $l_1$ and $l_2$, anchored at points $p_1$ and $p_2$ respectively (hence $p_2$ is time-variant), where the first rod is at an angle $\...
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Height of a mass swinging on a rope
The adjoint figure shows blocks of masses (assumed identical) rotating in a circle and they are binded by strings. We can see that the angle of inclination is increasing as we are moving to the left. ...
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$LC$ Oscillations [duplicate]
I understand the mathematics behind LC and RLC oscillator circuits in terms of setting up the second order differential equations and solving them, giving us the expected sinusoidal results, but I don'...
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Linear air resistance on a pendulum
I am investigating whether the air drag on a pendulum is linear. To test this, I used the solution to the differential equation of a damped pendulum(with $-kv$) and applied a Hilbert transformation to ...
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Is Rabi cycle a coupling of laser-atom as two resonators? Are photons travelling in both directions there?
Trying to understand Rabi cycle, I thought it resembles coupled pendulums/resonators like in the animation - wanted to ask if it is appropriate analog?
laser is large pumped directional resonator,
...
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The form of Euler-Lagrange equation $f''(t)+2\lambda f'(t)+\omega ^2 f(t)=0$ [duplicate]
Proof that differential equation $f''(t)+2\lambda f'(t)+\omega ^2 f(t)=0$ when $\lambda\neq0$ is not an Euler-Lagrange equation.
The damped harmonic oscillator equation with a dissipative force ...
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When do forces result in oscillation of oscillator?
I recently learned about the Cavendish experiment, which is used to find the Gravitational constant $G$. In short, two masses $m$ are put on the opposite sides of a balanced metal bar which hangs from ...
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Why is the potential of a pendulum $mgh$?
In all pendulum examples I've (assuming motion on the xy plane and no small angle approximation) textbooks say $\frac{1}{2} m (\dot{x}^2 + \dot{y}^2)+ m g y = constant$.
However, why is the potential ...
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Finding the Air resistance coefficient for a simple pendulum
We are conducting an experiment to approximate the air drag coefficient for a simple pendulum using objects of various shapes, such as a cylinder, a cube, and a sphere. One idea we had was to ...
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Question regarding two swings
Suppose I have two swings which are of the same weight but one has longer arms than the other, if I push one with some force (say x N)it does a full rotation and stops. By a full rotation I mean that ...
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Independence of generalized coordinates [closed]
In double pendulum when θ1 (the upper angle with vertical) changes it causes an eminent change on θ2(the lower one) which implies that they are not independent how can they still choosen for ...
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What is the efficiency of a Franklin's Bells device?
Just sitting here day dreaming, and I had a hypothesis that a Franklin's Bells device is likely extremely efficient. Its mostly a gut feeling though based on its low surface area contact point between ...
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Metronome oscillation and a scale?
Metronome oscillation
I have a question. Imagine a board but perfectly balanced on a single rolling point in the middle (for example only one can) and 2 identical metronomes at the two ends (all ...
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Period of Pendulum?
Does anyone know why curved lines from $\vec {OA}, \vec {OC}$ are curved? Is there some other property in the image below that is defining above mentioned curved lines in this picture?
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Two answers to one problem, but both seem correct (mathematically) [closed]
The question is:
Two particles are performing SHM along the $x$-axis and about the origin. If the maximum separation between them is equal to their amplitude $A$, find the phase difference.
Method 1-...
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Why is $Δω=R/L$ in quality factors derivation?
I was studying the derivation of quality factor and bandwidth regarding what it is. There it was written
$$Q=\frac{\overset{\tiny \blacktriangle}{\omega}}{\Delta\omega},$$
where $\overset{\tiny \...
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If you hold a pendulum and make it move in a circle, is that termed rotation?
What is the correct term to describe circular movement of a hand held pendulum? If you hold a pendulum that is hanging from a string and then force the pendulum to make circular motions, is that ...
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Does $x(t) = a \sin^2(\omega t+c)$ represent a Simple Harmonic Motion or not?
I had a doubt about the equation
$$x(t) = a \sin^2(\omega t+c).$$
Does this equation represent a Simple Harmonic Motion or not?
I did try it myself with 2 methods:
using trigonometry
using the ...
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Linear Triatomic Molecule
I am self-studying classical mechanics from the 3rd edition of Goldstein's Classical Mechanics. Right now, I'm working on Chapter 6, Problem 5, in which we are asked to consider a linear triatomic ...
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What is the criterion for oscillatory motion?
A ball bouncing (consider ideal elastic collisions) moves to and from about some point, but there is no equilibrium position. This motion sure is periodic... but is it oscillatory?
What is the ...
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In sand vibrator why is the normal force greater than weight below equilibrium position?
In a sand vibrator, as we go downwards, the normal force increases upwards, and as we go upwards, the normal force decreases just to the point that the sand loses contact. I know the proof of this ...
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Two alternate sets of governing equations for inverted pendulum
I've been scratching my head at these two tutorials, which achieve different governing equations for an inverted pendulum on a cart.
M is mass of cart, m is mass of pole, x is position of cart, $ \...
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Approximations when applying conservation of momentum to massive objects
I was solving the following problem, when I had this doubt, even though I solved it correctly I didn't quite understand the approximation I used to get the answer.
A small ball of mass $m_0$ is ...
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Equations of motion for n-coupled pendulum system
With reference to this article (https://drive.google.com/drive/u/0/mobile/folders/1d-IF8FTyizKHbaHXjVSxfaB3bgciqi4p),
the author uses 2n equations, where n is the number of pendulums, to describe the ...
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IMAT 2024 question about a moving pendulum seems to be wrong [closed]
Here is the question from IMAT 2024:
A pendulum rod moves from the vertical position. Which of the
following statements is false?
A) In the absence of friction, the
pendulum tends to come to a stop ...
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Degree of Freedom and Equations of Motion [duplicate]
I am a bit confused about the number of degrees of freedom of a simple pendulum. Is there
only angular displacement, or
angular displacement and angular velocity?
Also, I am a bit confused on the ...
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Goldstein Chapter 6 Question
I have a question about a potential error in the $3^{\mathrm{rd}}$ edition of Goldstein's Classical Mechanics. In their exposition in Chapter 6 of small oscillations, the authors obtain the usual ...
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Difficulty Achieving Stable Alternate Phase Synchronization (APS) in Metronome Synchronization Experiment
I am doing an experiment regarding the synchronization of two metronomes. My setup consists of two metronomes and a platform and cans. I place the platform on top of the cans and the metronomes on top ...
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Beat frequency equation of coupled pendulums with same natural frequency displaced to unequal extents [closed]
When 2 pendula of same natural frequency connected by a common spring are displaced to unequal extents, I understand that this causes the superposition of 2 normal modes: Parallel and symmetrical, ...
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Centripetal force
Assume a rotating table which is at rest, a inextensible , massless thread it suspended below table , on the other end is a bob of some mass, now the system is at rest thread vertically downward with ...
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Boundary conditions for massive spring hanging vertically [closed]
I was trying to to find the poistion of the center of mass of a massive spring hanging vertically under the effect of gravity and I tried to model it with a finite number of springs attached ...
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Term in double pendulum derivation
I'm working through a particular derivation of the equation of motion of a double pendulum of two points masses m1 and m2 with lengths $l_1$ and $l_2$ using angles off vertical $\theta_1$ and $\...
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What really is natural frequency and resonance?
Shouldn’t the frequency of an object depend on how much I push it from one end if the other end is attached?
And what’s resonance? In my textbook there is no such explanation to what is actually is ...
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Interpreting the magnitude of vectorial phasors
In fields of physics such as acoustics and electromagnetism, we often deal with physical quantities that are both vectorial and oscillating. These can be represented as vectorial phasors,
$$
\vec{b}(t)...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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{\...
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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 ...
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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} \...
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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.
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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
$$...
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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. ...
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