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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Rule swing with spring experiment: how can I modify it?

Basically I want to replicate this experiment (https://youtu.be/GqPGbHq2fxU). It's a ruler oscillating with one fixed end and one end attached to a spring. In my previous experiment, I used a short ...
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What are the best intuitive books to learn in-depth about waves and oscillations? [duplicate]

I was looking for a book/s that does not necessarily use a textbook-esque approach (e.g just providing definitions, equations, and examples) but dives deeply into the philosophy behind their mechanism,...
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How to correlate the frequency of source to The frequency of particle just between the two medium while transmission and reflection of wave?

When a pulse travels through rarer to denser medium,two new waves (reflected and transmitted) are formed from incident wave,While the wavelength of the Transmitted wave differs from wavelength of ...
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What curve does a stiff whisker flexing in oscillation due to inertia express? [duplicate]

Take a short length of stiff but flexible straight wire (I used ~5cm of ~0.1mm diameter brass) and hold it tightly at the base, then flick the tip. The wire will then rapidly oscillate in flexing back ...
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What is and what isn't considered an oscillation? And why?

If oscillations are periodic motions, is circular motion of an object with constant velocity also considered an oscillation, even though absolute value of its velocity and its acceleration are ...
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Conservation of energy while swinging on a swing without slack

So I have an issue with the following classical problem: Let's say you are on a swing of length $l$ hanging downwards, and you get pushed in a horizontal direction with speed $v_0$. How large should ...
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Is there any concept of "time difference" between oscillations(with same angular frequency) ? If yes, then how do I visualise it? [closed]

I encountered this question - "Two particles are oscillating along two parallel lines, with the same frequency and amplitude. They pass each other, moving in opposite directions when their ...
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A rule for when phase-space orbits may cross

Note: in this question when I talk about "phase space," I will be refering to velocity vs. position space, which can also be correctly referred to as "state space." Many sources (...
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Condition for true periodicity

In Vibrations and Waves, French writes that The condition for any sort of true periodicity in the combined motion is that the period of the component motions be commensurable- i.e., there exist two ...
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Kinetic energy of double pendulum

using cartesian coordinates as an intermediate step, the kinetic energy is calculated as such why is it incorrect to just say that the kinetic energy for the first bob is $$T_1 = (1/2) m_1 (l_1\dot{\...
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Critical damping oscilations - Equation in Fowles book

I'm not understanding a passage in the Fowles's book, seventh edition, equation 3.4.9. I understood that, considering: $x$ = position $\gamma$ = damping factor ${w_0}^2$ = k/m, where k is the ...
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Confusion with the concept of stable equilibrium of pendulum at resting position

According to my understanding, an oscillating pendulum is not at equilibrium, since its momentum and velocity changes with time. Now my question is that we say that the pendulum at its resting ...
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System where Energy Dissipates but Frequency Increases

Is there any example of an oscillating system where, as energy is dissipated by some external force, the frequency of the system's oscillation increases? One of the questions from 2022's IYPT asked ...
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Phases of vectors

This maybe because I am missing a whole concept itself, but how can vectors have a phase? I have been studying forced oscillations and I read that when multiplying a vector with i (sqrt(-1)) , the ...
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Derivation of Wave equation for general membrane

I am trying to derive the wave equation for a membrane of general shape from Hamilton's principle: $$W(u)=\int_{t_1}^{t_2}(T(u,t)-U(u,t))dt$$ and $$\frac{d}{ds}W(u+s\phi)|_{s=0} =0$$ The kinetic ...
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What would happen when two wave functions intersect in a Fourier series representation of periodic signals? [closed]

I saw a piece of code on github which transforms the planetary movement into the fourier wave function. These circles are given by the x and y ordinates: x=cos(ωt) y=sin(ωt), which are periodic. ...
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Confusion regarding oscillation of water in a straw

A drinking straw is dipped in a pan of water to depth $d$ from the surface (see figure below). Now water is sucked into it up to an initial height $h_0$ and then left to oscillate. As a result, its ...
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4 answers
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What is the motion of a pendulum for large angles? [duplicate]

We are given the second-order (non-linear) differential equation describing the pendulum $$\ddot x + \frac{g}{l}\sin(x) = 0.$$ One usually approximates this physical system with the one in which the ...
2 votes
2 answers
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Do protons or neutrons oscillate? (inside nucleus in atom)

Do they oscillate relative to each other? What is the frequency? What is the amplitude? I would think they oscillate since electrons move all over the place at high speeds and there is attractive ...
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3 answers
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Issue expanding $\sin \theta$ about $\theta_{eq}$

Quoting a textbook: $$(m_1 + 2m_2\sin^2\theta)\ddot\theta = m_1\Omega^2\sin\theta\cos\theta - \frac g L (m_1 + m_2)\sin\theta.\tag{10}$$ We can simplify this expression a bit by relating $\frac g L (...
1 vote
2 answers
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Non-conservative force, but equation of harmonic motion

A small disc is projected on a horizontal floor with speed $u$. Coefficient of friction between the disc and floor varies as $\mu = \mu_0+ kx$, where $x$ is the distance covered. Find distance slid by ...
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1 answer
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Fourier Component And Resonance

Wikipedia defined Resonance as the following : Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is ...
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Non-swinging Foucault's pendulum

If there is a stationary pendulum, say at the North pole, neglecting torsion, etc. will it seem like spinning around its axis from the reference frame fixed to the Earth's surface. If so, will it ...
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Problem 6.3 from David Morin (classical mechanics) [closed]

I get the lagrangian for the system as $$ \begin{align} \mathscr{L} = \frac{m}{2}(\dot{x}^2 + l^2\dot{\theta}^2 + 2l\dot{x}\dot{\theta}\cos \theta) + mgl\cos\theta \end{align} $$ Where $\theta$ is the ...
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Lagrangian and Action for a plane pendulum under the dampling force exerted by air resistance [duplicate]

Consider a plane pendulum which is composed of an ideal string and a sphere of mass m and length $l$. As a consequence of the presence of air, it exerts a force proportional to the speed characterized ...
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If a particle is performing simple harmonic motion and the speed of particle is increased then how it's gonna effect it's angular velocity?

The question was A particle is performing SHM and it's speed is tripled at some distance, find the new amplitude? So, while solving the question my teacher said, angular frequency won't change when ...
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3 answers
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For a simple pendulum does the size of bob need to be small w.r.t. the string to be considered as harmonic oscillator? [closed]

if a simple pendulum has a bob with radius comparable to a string can it still be considered as shm given the amplitude is small?
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Lagrangian of inverted physical pendulum with oscillating base

An inverted physical pendulum is deviated by a small angle $\varphi$ and connected to an oscillating base with oscillation function $a(t)$. The pendulum's mass is $m$ and its center of mass is $l$ ...
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How to get the limit cycle of a nonlinear oscillator using Shooting Method?

I am trying to find the limit cycle of a nonlinear oscillator like a duffing or Van-der-Pol oscillator directly using the shooting method. I know how to use the Shooting method to solve a Boundary ...
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3 votes
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How exactly can we shake an object to determine its mass?

It's often said that inertial mass is a measure of how hard it is to shake an object (as distinct from gravitational mass, which is how hard it is to lift an object in a gravitational field). Because ...
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Displacement relation of a progresive wave

I know that the displacement relation of a body in simple harmonic motion (SHM) is given by $$x(t) = A\cos(\omega t+\phi)$$ Displacement relation of a progressive wave is a similar one: $$y(x,t) = A\...
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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....
9 votes
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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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1 answer
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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 ...
3 votes
1 answer
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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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2 votes
2 answers
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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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2 answers
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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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1 answer
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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 ...
7 votes
5 answers
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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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