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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Oscillator with non-linear damping - question re a specific approach
The following paper
https://core.ac.uk/reader/82037870
Oscillators with nonlinear elastic and damping forces
L.Cveticanin
studies the general problem
$$ \ddot{x} + 2 b_k \, \dot{x} \, |\dot{x}|^k + \...
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If perturbation theory applies to the pendulum, can it also apply to string vibration?
The pendulum and string seem to prove the adage “frequency and amplitude are independent.” Frequency does not vary with time but amplitude decays onto an equilibrium position. The amplitude is a small ...
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Is sound essentially motion?
From my understanding, the only way for humans to create sound is by moving our bodies, vocal cords, or by moving other objects. So depending on how fast we or other objects can move, different ...
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Oscillator with non-linear damping / drag equation
For linear damping
$$ \ddot{y} + 2\beta_0 \, \dot{y} + \omega_0^2 y = 0 $$
the solution with initial conditions $y(0) = y_0, \; \dot{y}(0) = 0$ reads
$$ y(t) = y_0 \, \sec\delta \, e^{-\beta_0 t} \, \...
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Is projection of a simple pendulum, doing SHM as well?
I know projection/shadow of a Uniform Cirular Motion does SHM, and a simple pendulum also does shm. But I was wondering whether, for a pendulum in $xy$ plane having its central axis parallel to $y$ ...
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How to prove the phase constant is $φ=\arctan(-b/2mω)$ in an underdamped system when the startin velocity is 0?
I have trouble with a minor part of my physics project. I need to show how you get that the phase constant is φ = arctan(-b/2mω) when I know the starting velocuty is 0 in an underdamped system. I have ...
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Numerically determining steady state in oscillating systems
As the title says, I'm trying to determine numerically when an n-DOF oscillating system (linear or nonlinear) subjected to forced base oscillation reaches the steady state solution.
Is there an energy ...
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Force-dependency of frequency response of driven harmonic oscillator with damping
For a driven harmonic oscillator with damping of the form
\begin{equation}
\ddot{x} + 2\xi\omega_0\dot{x} + \omega_0^2x = \frac{F_0}{m}cos(wt)
\end{equation}
with damping ratio $\xi$ and natural ...
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Approximate Solution to Damped Nonlinear Pendulum
The Nonlinear Damped Pendulum Equation
$\ddot{\theta}+\frac{b}{m}\dot{\theta}+\frac{g}{l}\sin(\theta)=0$
isn’t exactly solvable unlike the Nonlinear Pendulum as there’s no constant of motion namely ...
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The frequency is off by a factor of $2 \pi$?
I was reading Morin's Introduction to Mechanics, and the following material came up:
At equilibrium point $x_0$ expanding the Taylor series, we see $V(x)=\frac12 V''(x_0)(x-x_0)^2$ so comparing this ...
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Solutions to critically damped harmonic oscillator?
From MITOpenCourseWare, I was learning about the damped harmonic oscillator. Some context is pasted below.
Case (iii) Critical Damping (repeated real roots)
If $b^2 = 4mk$ then the term under the ...
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Steady-state of an expectation value of an oscillator system
For context, I am dealing with an equation of motion for the expectation value $\beta=\left\langle\hat{b}\right\rangle$ of a quantum van der Pol oscillator. But I would love a more general explanation....
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In a damped oscillation with damping force $F=-bu$ at which position does the maximum velocity occur?
In a SHO we know that V will become a maximum in the equilibrium position with V= Aω. Does the same apply to a damped oscillation with the damping force being F=-bu or is the position somewhere else?
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Show that $dE/dt = -bv^2$ (Help with differentiation) [closed]
The question is:
Show that $$dE/dt = -b (dx/dt)^2.$$
And the solution is:
...
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Analytic description of oscillations in a rotating frame of reference?
Imagine you have a pendulum attached to a rotating axis. You define two frames of reference. In the $S$ frame, the pendulum is oscilating and rotating around this axis. The $S'$ frame is define such ...
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Does rhythm create pitch?
As in,
matter (a physical object)
that is vibrating
= a pitch
And secondly
If we calculate bpm with a “tick” which is just indefinite pitched percussion, how does an indefinite pitched beat compare to ...
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Natural Harmonics on a String
Consider the Dirichlet boundary value problem of a guitar string stretched between two fixed points which is made to oscillate by pinching and releasing the string.
It can be shown in quite ...
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Neutrino oscillations and neutrino mass measurement
At the KIT they have been measuring the mass of the electron neutrino with a huge spectrometer (i.e. they make an enormous effort) and already published limits on the highest possible electron ...
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Deriving the Exponential Decay Rate in Damped Oscillation
I am currently working on this book: https://openstax.org/books/university-physics-volume-1/pages/15-5-damped-oscillations
The position as a function of time for damped oscillations is given by $$x(t)=...
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Derivation of time period for physical pendula without calculus [closed]
I need to derive the following equation, ideally without using calculus:
This website ( http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html#c1 ) has a good derivation but skips an important step at ...
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Determination of exponents in physical pendulum equation of oscillation period
Physical pendulum oscillates with a period that can be described by the equation: $T=2\pi I^{\alpha}m^{\beta}g^{\gamma}d^{\delta}$, where the exponents are all non-zero. The units are: $T\,[s]$, $I\,\...
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Meaning of short, medium and long baselines
I was reading about the experiments on Neutrinos and came accross terms like "Short", "long" and "medium" baseline experiments. Can anyone please tell me how do we define ...
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"Natural frequency" seems to be a poorly defined concept [closed]
Per wikipedia: natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force.
Let's take a wine glass as an example.
The ...
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Connecting rotational period with period of oscillation
Recently I have been thinking about if rotational period is somehow related to period of oscillation for SHMs. My original question was how velocity of something impacting a spring affects its ...
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Fourier Transform of Damped Oscillations - Zero Frequency Peak and Shift [duplicate]
A damped oscillator has the time evolution:
$$ y(t) = e^{-\Gamma t}\cos^2(\tilde{\omega}_0 t)$$
where $\Gamma$ is the damping rate, $\tilde{\omega}_0^2=\omega_0^2-\Gamma^2$ and $\omega_0$ is the ...
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How can I calculate accurate energy loss that occurs in a compound pendulum?
I want to find out the energy loss that occurs in a compound pendulum. Is simply using the $(1/2)mv^2$ formula suitable ($(1/2)mv^2$ of after and before)? Or is there a more accurate way?
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Can mechanical waves exist in zero gravity?
Just got out of a test and there was this question asking of true/false:
“A fluid presents pressure variation only when subjected to a gravitational field”
To which the alleged correct answer was “...
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How to determine structure stiffness of a damped 1D system with acceleration - time graph?
Consider a damped system with only acceleration - time data is available, how to determine the structure stiffness (k)? Mass of the structure is also known. It moves in a horizontal direction, like a ...
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Question about condition for oscillation of a physical system in Lagrangian mechanics
I can't answer the following question about a (simple) physical system I have studied using Lagrangian mechanic techniques.
So, we have a straight rigid rod in a horizontal plane, symmetrically fixed ...
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A bouncing ball is bouncing elastically then it is SHM or not?
A ball is bouncing elastically after its collision from ground so can we call it SHM as it is oscillating and also it is periodic and it seems similar to other cases of SHM? If yes then where is it's ...
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Damping of a pendulum through air and magnetic field (eddy currents)
So as part of a project, I am investigating how the damping coefficient changes as the surface area of a metal sheet increases. As it increases, intuitively so do the eddy currents generated and so ...
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Amplitude of a Damped Harmonic Oscillator
Background: What I know about simple harmonic oscillators
For a simple (undamped) harmonic oscillator, one expression for the position as a function of time is
$$
x(t) = x_0 \cos(\omega_0 t) + \frac{...
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What is the meaning of an imaginary part of position in Lorentz-Drude model?
Some time ago I got to know about Lorentz-Drude model, which predicts dependence of complex permittivity $\varepsilon = \varepsilon_1 + i \varepsilon_2$ from classical assumptions.
In the model, ...
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Bubble phenomenon
A few days ago I encountered a problem that caught my attention:
The surface of an air bubble oscillates at a frequency of $20$ kHZ. We
observe that this oscillation causes another air bubble nearby ...
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Equation of motion for a driven mechanical oscillator
I'm trying to derive the differential equation for a driven horizontal mechanical oscillator.
If I suppose that a spring is fixed at one end and attached to a solid at the other end and that the solid ...
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Effect of the length $\ell$ on a pendulum
Currently, I am trying to intuitively understand how the length $\ell$ affects the period of a pendulum. I understand that the shorter the length $\ell$, the shorter the time period $T$. When we have ...
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What is the role of fictitious force in simple harmonic motion?
While I was searching about simple harmonic motion, Wikipedia defined it as,
"In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion of ...
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Complete Solution to Damped Pendulum Second-Order Differential [duplicate]
Of all the pages I've read on this stack exchange, I've seen numerous proofs and comments on the complete solution to the period of an undamped pendulum, and they all involve complete elliptic ...
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Damped harmonic motion experiment, bad results but good statistics
I've done an experiment with a pendulum swinging at very small angles. I added an object with the shape of a rectangle to it, to increase the air friction to create damped harmonic motion.
This is the ...
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How we can study sinusoidal rectilinear motion? [duplicate]
I don't understand rectilinear sinusoidal motion well, for exemple if I have the time of achieve the end of the trajectory how I can find the period T to calculate Omega? I really need a text book to ...
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Time period of a simple pendulum confusion
While calculating the time period of a simple pendulum, i.e $$T=2\pi\sqrt{\frac{L}{g}}$$
Why do we consider the effective length, $L$?
It is the distance from the point of suspension to the centre of ...
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Can a pendulum have detectable harmonic frequencies
Can a pendulum produce harmonic frequencies? Like could I detect harmonic frequencies if I had a sensor on the pendulum?
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References for harmonic oscillator with memory
I'm reading Neu's "Singular Perturbation in the Physical Sciences" and in problems 1.1 and 1.2 he defines systems that "have memory" as the the variant of the harmonic oscillator
$$...
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Construction of lissajous figure from equation [closed]
So I was solving questions from my workbook and came across this problem. I don't know how to solve this.
QUESTION: Two vibrations at right angles to one another is described by the equations x=10cos(...
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Question in time period of oscillation of a ball in bowl [duplicate]
We know time period of pendulum is $$T=2\pi\sqrt{\frac{L}{g}}$$
While reading through a question on S.E which was based on a ball oscillating on a bowl , I was curious and I thought of its time period ...
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Occurrence of *critical* damping
I am trying to understand the origin of some transient signals the vast majority of which have shape $(t/\tau) \exp(-t/\tau)$ for $t\gt 0$. This is notoriously the impulse response of a critically ...
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Energy conservation in a driven harmonic oscillator
The ODE for a driven harmonic oscillator is given by
$$
\ddot{x}+2\gamma \dot{x}+\omega_0^2 x = \frac{F}{m}\cos(\omega_dt)
$$
By assuming balance of forces, i.e. energy conservation, one can solve for ...
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How did Léon Foucault showcase his Foucault's Pendulum?
When I was thinking of Foucault's pendulum , this question was always bugging me. If we are all rotating with the same speed in one reference frame as the surface of earth with the pendulum , then the ...
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Three dimensional classical continuum limit, wave equation
Many textbooks of classical mechanics or classical field theory mention that a three dimensional "string" (the continuum limit of a lattice) leads to/can be described by the 3 dimensional ...
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Formula for Bifilar Pendulum
What is the formula for a Bifilar Pendulum's Period? Assuming the Pendulum oscillates sideways. ( Spins to the left and then to the right etc. ). I can't seem to find the formula online.
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