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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What does the position $x(t)$ looks like in an overdamped system?

I know that for the position $x$ as a function of time in an underdamped system (such as a mass on a spring) you can use the function: $$x(t)=Ae^{\gamma t}cos(\omega t-\phi),$$ where $$ \begin{split} ...
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Equation of motion of a particle in a sinusoidal well

Do you have solutions for the (classical or not) equations of motion of a particle in a sinusoidal well or just a quartic well, classicaly I would write the equations like so: $$\frac{d^2x}{dt^2}\...
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Motion of an $n$ mass $n$ spring system [closed]

While reading wave motion I encountered the problem of $n$ identical masses with $n$ identical springs in between them. If we give a sudden push to the wall attached to the first spring, what will ...
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Oscillating solutions to Friedmann equations

Does homogeneous and isotropic Friedmann cosmologies allow for periodic (simple harmonic solutions) Universes? Can they (universal oscillators) solve the issue of the initial (or future) singularities?...
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Would it be correct to state that the damping force and the spring force are equal in the case of critical damping?

(Note: this question is for a spring mass system moving through air) Intuitively it makes sense to me that they would be equal to each other, but I have not found a clear answer referencing the forces....
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Intuition behind the differential equation for forced oscillations

The differential equation for forced oscillation is: $$m \ddot{x} + b\dot{x}+kx = F_{o}\sin(\omega''t)$$ I don't find this equation intuitively satisfying. My mind tends to think that as $F_{o}\sin(\...
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What's the amplitude of the energy loosing oscillator as a function of time?

The problem comes from 'introduction to classical mechanics' by David Morin. It is as follows: A chain with mass density $\sigma$ kg/m hangs from a spring with spring constant $k$. In the equilibrium ...
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How to describe a series of damped harmonic oscilators?

I am looking for textbooks or papers that provide an analysis for a series of damped springs. I am having a tricky time working out the details on my own. I know that if $F=-k\Delta x$ a series of ...
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Coupled Oscillator Period [closed]

I was studying an example of a coupled oscillator the other day, namely two identical masses attached to three springs, the lateral ones of which with the same elastic constant, when I came across the ...
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On the behavior of critically damped oscillators [duplicate]

Is a critically damped oscillator always going to approach the equilibrium position faster that the same system with underdamping or overdamping for a given set of initial conditions, no matter what ...
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At resonance, there is infinite oscillation (new)

As per a previous question: Transient behavour For a driven harmonic oscillator: I was trying to show an exponential increase in amplitude using the transient solution, however I still got the sake ...
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Does amplitude really go to infinity in resonance?

I was recapping the forced oscillations, and something troubled me. The equation concerning forced oscillation is: $$ x=\frac{F_0}{m(\omega_0^2-\omega^2)}\cos(\omega t) $$ I don't understand why this ...
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The motion of a spring due to wind (Wind induced oscillations)

Consider a spring held in the direction of wind as shown in the image. the spring body is wrapped with paper so that the spring oscillates with the wind in a circular manner. Is there any mathematical ...
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Kinematics of a rolling disk on a static disk (variation of the Euler disk)

I'm puzzled by the following problem. Consider a simple tilted disk $\mathcal{D}$ of radius 1 (in any unit) rolling without sliding on top of a static horizontal disk $\mathcal{S}$. The normal $\...
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Simple pendulum using plane polar coordinates: where did I miss a minus sign? [closed]

Suppose we want to write the equation of a simple pendulum using plane polar $(r,\theta)$ coordinates with the point of suspension as the origin and with $\theta$ increasing anticlockwise from the ...
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Time period of spring pendulum

If in a car moving on circular path (uniformly with speed $v$) a spring pendulum is suspended then why is its time period independent of $g$ and acceleration of car even though both gravity and pseudo ...
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Why is there a difference between single and double compound pendulum's kinetic energy equation?

When calculating equation of motion of single compound pendulum, kinetic energy is taken as $K= I\dot{\theta}^2/2$ (See). But when it is double compound pendulum, kinetic energy of the first pendulum ...
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Does this question have two answers correct?

A simple pendulum (whose length is less than that of a second's pendulum) and a second's pendulum start swinging in phase. They again swing in phase after an interval of $18$ seconds from the start. ...
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Modeling an inverted pendulum but with motion of the cart stabilized by an external force

I would like to model an inverted pendulum on a cart with a little twist. For starters the cart has a motor that generates a force and applies it to the wheels. We can calculate the equations of ...
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What causes the lamp above my gas stove to swing like a pendulum when the stove is on?

There is lamp hanging above my gas stove, which when the stove is turned on performs pendulum-like oscillations in an oval trajectory, not unlike the dynamics of Lissajous patterns. The lamp is ...
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Why doesn't angular frequency change in damped simple harmonic motion?

I recently carried out an experiment varying different factors affecting simple harmonic motion, namely friction and air resistance. Whilst carrying out research for this, I found the relationship ...
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Parallel and Series Oscillator in Mechanics

In the electrical domain two types of (damped) oscillator exists: series oscillator: coil, capacitor and resistor are connected in series; the current through each element is the same and the ...
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How is there kinetic energy at the bottom of the pendulum swing if velocity = 0 at the lowest point?

Say a mass $m$ is attached to a massless string that is attached to the ceiling. The mass is pulled 30 degrees to the left of the vertical and then let go. At the lowest point of its swing it has ...
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Lagrange Equation for a physical pendulum attached to a spring

I have a very specific problem and need a lagrangian equation and differential equation for the motion of mass $m$. The center of a metal rod with length $2R$ is attached to a ball bearing so it can ...
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Graphing the motion of a driven damped pendulum

$ \ddot{\phi}+2 \beta \dot{\phi}+\omega_{0}^{2} \sin \phi=\gamma \omega_{0}^{2} \cos \omega t$ The equation of movement is written above. I´m trying to plot the value of $\phi$ for different values of ...
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Finding angular frequency via integration of Newton's Second Law for a physical pendulum

For context: I am a student enrolled in AP Physics C with prior knowledge from AP Calculus AB and AP Physics 1. We just collected data for a lab to determine an experimental value for g. The setup ...
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Energy of a system executing forced oscillations

In L&L's textbook of Mechanics (Vol. 1 of the Course in Theoretical Physics) $\S 22$ Forced oscillations, one finds the following statement: \begin{equation} \xi = \dot{x} + i \omega x, \tag{22.9}...
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Definition of Quality Factor $Q$

The stored energy definition of the quality factor $Q$from wiki Q-factor from wiki is given by $$ Q = 2\pi \frac{\text{energy stored}}{\text{energy dissipated per cycle}}= 2\pi f_0 \frac{\text{...
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Simple harmonic oscillator in a rocket which accelerates upward [closed]

I'm working my way through a textbook that deals with differential equations. Here's a problem that I need some help to solve: Suppose a spring with a constant 4.5 kg/sec² is attached to a body with ...
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Energy dissipated during cycle of damping force

Considering a drive damped oscillator after transients have died out and is being drive close to resonance such that $\omega=\omega_0$, I want to find the energy dissipated during one cycle, $\Delta ...
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Expression for Steady state of Forced vibration [duplicate]

In my book under the topic Steady state of the forced oscillator, they started with the equation: $$\frac{d^2x}{dt^2}+γ\frac{dx}{dt}+ω_0^2x=fe^{jωt}$$ I know the equation for damped oscillation but it ...
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Energy delivered to unstable limit cycle

For a given family of stable and unstable $T$-periodic limit cycles $\Gamma$ forming a manifold $\mathcal{M}\subset \mathbb{R}^n\times \mathbb{R}^p$ of some (nonconservative) $p$-parametric $n$-...
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When a ball is dropped on a floor is that harmonic motion?

From Simple Harmonic Motion, we conclude that acceleration is proportional to its distance and the sign is negative. We also know that at equilibrium position $dU/dx=0$. Now, if we think a ball is ...
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How to obtain the eigenvalues of Hamiltonian $H=p^2+x^2 (i x)^{\epsilon}$?

For quantum harmonic oscillator Hamiltonian $H=p^2 + x^2$, one can calculate the eigenvalues $(2n+1)\omega/2~$ ( with $\hbar =1).$ Now I came across this Hamiltonian $$H=p^2+x^2 (i x)^{\epsilon},\tag{...
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How does damping constant relate to mass?

(Moderator note: this question is not answered by a different post here) In damped harmonic motion, I'm led to believe that the equation of motion in a mass-spring system is as follows $$x = Ae^{-λt} ...
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1 vote
1 answer
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Self-synchronizing and -desynchronizing systems of oscillators

There are biological systems with adaptable frequencies that are able to synchronize their frequencies, mainly individuals (see e.g. reproductive synchrony). In this case, also the phase is typically ...
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3 answers
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Can uniform linear motion be considered as periodic motion?

According to some definitions of periodic motion on internet as well as in my book: Motion repeated in equal interval of time is called Periodic Motion. Now, if I am in uniform linear motion my ...
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Particle Coupling in Ion Trap

Ion traps are very complex, but one of my Physics Olympiad textbooks presents a simplified model of a resonating charged particle in an ion trap A tuned circuit consists of an inductor and a parallel ...
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Is there any known result about the "average period" of a complicated oscillating function?

Say we have some frequency spectrum, $f(\omega)$, where $$ f(t) = \frac{1}{2\pi} \int_{-\infty}^\infty d\omega \; f(\omega)e^{-i\omega t}, $$ and we know that $f(t)$ is some sort of ...
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Lagrangian of an elastic pendulum

I'm trying to understand the way my teacher found the Lagrangian of an elastic pendulum. Given a spring pendulum connected to the origin, the equilibrium point is $(0,0,\frac{-mg}{k})$. The length of ...
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Oscillations in a Time-Varying Magnetic Field

Suppose we have a cantilever (with a magnetic moment/charge attached to one of its ends) oscillating in a magnetic field which is spatially varying in the $x$ direction and is also time dependent, ...
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4 votes
1 answer
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Considering General Relativity, how long would it take for a ball to stop oscillating dropped through the center of the Earth?

In Newtonian view, if a relatively small mass was dropped through a frictionless tunnel without drag intersecting the center of a non-rotating, spherically symmetric,uniform density Earth, then the ...
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1 vote
2 answers
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Why is amplitude going to infinity in forced damped oscillator at resonance?

I'm trying to find the amplitude of steady state response of the following differential equation: $$\ddot{x}+2p\dot x + {\omega_0}^2x=\cos(\omega t)$$ A particular solution is $$x_p=\Re{\dfrac{e^{i\...
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Why is Angular Frequency $ω=2π/T$?

I've seen in many books, internet and video lectures, that equation of SHM: $$x(t)=A\cos(\omega t+\phi)$$ where they just say that (without telling anything about $\omega$): $$\omega=\frac{2\pi}{T}$$ ...
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What is the difference between non-linear oscillator and non-uniform oscillator?

The equation for a uniform oscillator is: $\dot\theta = \omega$ which has a solution of $\theta(t) = \omega t +\theta_0$. For a non-uniform oscillator, the equation is: $\dot\theta= \omega - a$ where $...
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Total energy in a superposition of many waves

Consider the superposition of $N$ waves of equal amplitude whose angular frequency lies in the interval $[\omega_1, \omega_2]$, emitted by an oscillator at $x=0$ where we take $\omega_2 - \omega_1=∆\...
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Solution to non-linear differential equation, non-linear oscillator

Is there any way to find an analytical solution to this equation? $$ m \ddot{x}(t) = B_0 \left( \frac{1}{x(t)^4} - \frac{1}{(L-x(t))^4} \right)$$ this is supposed to describe a magnetic oscillator ...
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3 answers
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Considering a pendulum clock does the period of oscillation of the pendulum increase when the clock itself is set in motion? [closed]

Considering a pendulum clock does the period of oscillation of the pendulum increase when the clock itself is set in motion due to increase of mass?
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2 answers
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Equilibrium positions of a tilted rod rotating around vertical axis

First of all, this is my first ever question on any forum so forgive me if it's not so well written. Second, I'm not a native English speaker so if there is any writing error, I'm sorry. The problem ...
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14 votes
7 answers
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Why does critical damping return to equilibrium faster than overdamping?

How can one prove that the critical damping regime returns to equilibrium fastest? Is it true that there are cases where the heavy damped solution will return faster? Consider a free harmonic ...
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