Questions tagged [oscillators]

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Lagrangian for nonlinear small oscillations

My original Lagrangian is this, but I want to obtain nonlinear terms considering small oscillations : $$ L = ma^2[\dot \theta^2(1+ 2\sin^2\theta) + \Omega^2\sin^2\theta + 2\Omega_0\cos\theta] . $$ ...
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What is the frequency of the oscillation? [closed]

Cheap shock absorbers in cars don't absorb energy and oscillate too long. Take for instance an ideal spring shock absorber that is set up in a vertical position for a 1100.00 kg car. When you, 900.00 ...
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Is gravitational Force is damping force in vertical mass-spring system of constant k in Simple Harmonic motion

When a block of mass m is suspended by vertical spring system,it for sure perform SHM in the absence of damping force,only force which act on the system is internal which is -kx, where k is spring ...
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3answers
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Expression for total potential energy in coupled systems

I was reading through applications of Lagrangian mechanics and the case of coupled oscillators. The example provided is the famous two pendula length $l$ mass $m$ hanging from the ceiling connected by ...
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3answers
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How can we be sure that the equation of SHM that works for one dimension of an object moving in circular motion works for all SHM?

I have learned that a component of a uniform circular motion is an example of SHM. And I have no question about it, I totally understand that. I also understand how we can derive formulas like $\vec{...
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2answers
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How does a drum's membrane oscillate?

I was thinking about a problem with a simple wooden drum , constructed but just a membrane and a wooden circular part .Let's say the mebrane is streched by a constant tension $T$ and it has a density ...
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Driving system with damping [closed]

Suppose that the displacement of the end of the wire vanishes for $t < 0$, and has the form $d\sin(w t)$, there is damping in the system. Find the displacement of the block for $t > 0$. Write ...
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Heat dissipation inside an extremely high inductive coil

Is it possible that for an extremely high inductive coil the oscillation paths for the electrons are so small that they can 'live' between atoms of the copper lattice without touch them and so not ...
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2answers
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Intuition behind forced oscillations

in every book I own and on the internet, any information on forced oscillations is a version of the following definition, followed by the solution to a differential equation. Forced oscillations: ...
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Dynamics of rod on two oscillating supports

I am trying to model a rod supported by 2 non-frictionless oscillating supports. In case the image is not clear, a rod of mass $m$ is resting on 2 frictionless supports that touch it at a point. The ...
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2answers
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How do I describe the following system? [closed]

So the professor of my physics 3 class assigned this problem regarding forced oscillations. A mass of 0.30kg hangs of a massless rope. The center of oscillation can move as shown in the figure. When ...
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Solutions to damped harmonic oscillator?

For the damped harmonic oscillator equation $$\frac{d^2x}{dt^2}+\frac{c}{m}\frac{dx}{dt}+\frac{k}{m}x=0$$ we get that the general solution is $$x(t)=Ae^{-\gamma t}e^{i\omega_d t}+Be^{-\gamma t}e^{-i\...
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Can the $Q$ factor of a system exceed unity ($Q>1$) while the maximum gain is 1?

when calculating the quality factor of an acoustic system using FWHM definition I get 39. the maximum gain is approximately (see the attached figure ). when I calculate $Q$ in time domain using the ...
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Normal Modes and Normal Frequencies - Matrix Notation

Can somebody share with me sources where I can study about this topic ? I want to study the natural modes of a system with multiple degrees of freedom (with lagrangian formalism) but in terms of ...
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What does the disconuity in the equation for modulated phase mean when superposing two SHM?

So I was working out the result of the composition of two SHM that are in the same direction and have different frequencies and amplitudes. Turns out I found the following equation for the modulated ...
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Energy transfer between oscillators [closed]

Suppose I have two mechanical oscillators $a(t), b(t)$, coupled through the interaction $V_\text{int} = \mu^2 a(t) b(t)$. Is there a simple way to express the rate of energy transfer from $a$ to $b$ ...
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Why does poured honey move periodically when reaching the surface it's poured upon?

Here's the picture, known to most of us: When honey is poured out of a container, as in the picture (look here for the flow in motion), we see a kind of periodic flow of the honey when it comes to a ...
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SHM phase relations between v,a,y

I was reading about the phase relation between the displacement , velocity and acceleration of a particle executing SHM.I understood that all three differ in phase by π/2 radian respectively . In my ...
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Derivation of angular frequency of underdamped harmonic oscillator [closed]

Why is the angular frequency of an underdamped harmonic oscillator given by:$$\omega_1=\omega_0\sqrt{1-\zeta^2}$$
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Deriving a model of a point-driven Chladni plate

Please note — this question considers a point-driven Chladni plate, not Chladni's classical experiment. I'm aware of various other questions concerning the latter here on Physics.SE. As the title ...
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2answers
39 views

How would you determine the point at which a object would lose contact with a oscillating bridge, given information?

I was recently going through question on Simple harmonic motion and came across the example in the photos i could do all the question until the last one which stated to show the time in which the dog ...
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1answer
56 views

Condition of SHM in rotational motion [closed]

A small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is the same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such ...
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5answers
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Why does mass-spring system tend or prefer to oscillate with natural frequency? Can you explain it theoretically rather the derived version of it? [closed]

Why the mass spring system prefers to oscillate at natural frequency, why does it rather oscillate at other frequencies? Every object in the universe is always vibrating, is it true? if it is the ...
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2answers
64 views

Simple harmonic motion in a non-inertial frame [closed]

For simple harmonic motion in a non-inertial frame is amplitude same on both sides? As in one direction pseudo force supports acceleration due to spring and in another direction it opposes ...
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In what sense is a quantum damped harmonic oscillator dissipative?

The classical Hamiltonian of a damped harmonic oscillator $$H=\frac{p^2}{2m}e^{-\gamma t}+\frac{1}{2}m\omega^2e^{\gamma t}x^2,~(\gamma>0)\tag{1}$$ when promoted to quantum version, remains ...
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Intrinsic oscillation

In this paper here It defines some time scales.in page 3 was said that $$ \tau_E^{-1}\equiv min |\epsilon_{mn}(t)| \quad ,m \neq n $$ where $ \epsilon_{mn}(t) ≡ \epsilon_m(t) − \epsilon_n(t)$ denotes ...
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Can sway be eliminated in the pendulum cart problem?

This problem is similar to the cart-pendulum problem. I have a cart and a mass attached to the cart via a weightless string. Both the cart and the mass are travelling at a constant speed in the same ...
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1answer
28 views

Oscillations of a vertical spring with non negligible mass

My physics professor recently covered the concept of simple harmonic motion and touched on vertical springs. However he mentioned that the spring (with a mass attached to its end) only undergoes ...
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1answer
33 views

Time period for small vertical oscillations of bob

We have a small bob attached to an elastic rubber wire and we are given values of the wire’s Young’s modulus, length, and area. My doubt is not to know the answer specifically, just to review my ...
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What's a normalized coupling strength?

While reading about elctron-phonon coupling, I came across the term normalized coupling strength. It was defined as $$\eta = g / \omega$$ where $g$ is the coupling constant and $\omega$ the ground ...
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2answers
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Changing length of Pendulum

Let's say we have a pendulum and with an initial displacement of 5 degrees, it starts oscillating. Assuming ideal conditions, the pendulum will oscillate forever with its maximum sway angle being 5 ...
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1answer
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Neutrino flavor and mass

Neutrinos with specific mass don't have a unique flavor and neutrinos with specific flavor don't have unique mass. Let's call the neutrinos with specific mass $\nu_1, \nu_2, \nu_3$ and the neutrinos ...
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Simple harmonic motion of a cylinder inside another cylinder [closed]

Hi guys! One quick note before diving into the question. When you are answering this question please consider me as a layman and be as thorough as possible. So, I have 2 cylinders; the smaller one ...
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2answers
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How can I express velocity as a function of position in a damped oscillation? [closed]

In a damped oscillation that obeys $x(t)=Ae^{-bt/2m}\cos(ωt)$ which shows the position of the oscillating object as a function of time, how can I express the velocity of the oscillating object as a ...
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1answer
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What happens if an electric dipole is placed in a non-uniform electric field?

I have viewed the question : An electric dipole placed in a non-uniform electric field But that is a different one from my query. I also viewed its answer. My question is if an electric dipole is ...
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Difference between vibration and oscillation considering a point in space

Most answers and articles I've read so far try to give real world examples such as a spring or a pendulum. However, I'm trying to understand the core difference between the two terms in the most ...
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2answers
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Quality factor definition

During my study of oscillators I have encountered two different ways do define the Quality factor $Q$, which gives information about the amount of damping on a system. Suppose the oscillator equation ...
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3answers
85 views

Forced oscillations

Suppose we are using a pendulum. From one extremity we just leave it, it reaches the other extremity and again reaches us at a certain time period. We will be able to apply the next force to it when ...
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What is the meaning of the angular frequency of a spring?

In this differential equation, $$ \ddot{x} + \frac{k}{m}x = 0 $$ We assume that $$ \frac{k}{m} = w^{2}$$ Why is that? And how one can prove it?
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Understanding Baryonic Acoustic Oscillations

I was reading the book of Barbara Ryden "Introduction to cosmology": In the chapter number 9, in the page 203. She says: "The photons, electrons, and protons together make a single ...
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1answer
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Long term solution for a driven harmonic oscillator

Let $F(t)= \cos (\omega_d t) $ be the driving force of a harmonic oscillator of mass $m$ which is damped with a damping constant $b$ such that $F= -bv $ is the damping force and the spring exerts a ...
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Will the motion of an Euler's disc be considered as oscillatory or simple harmonic motion?

Can the motion of an Euler's disc be described similar to that of a compound pendulum ? or any other type of oscillatory motion ? I was studying simple harmonic motion and oscillation and came across ...
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1answer
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Are all orbits of the conservative pendulum homoclinic?

I don't understand this statement: "The homoclinic orbit is characterized by $E = mgl$. When $E < mgl$, the pendulum is tracing other orbits." If energy is conserved, then $E_0 = E$ ($E$...
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Damped harmonic oscillation (LC circuit)

The $LC$ circuit I'm considering contains a capacitor, an inductor and an electrical resistance. There is no battery: intially the capacitor has a charge $Q$ and the electric current in the circuit is ...
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3answers
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Is every oscillatory motion periodic in the absence of damping?

Well, I asked this title question to my teacher, and he told me that yes, it is true. But I couldn't quite understand how is it possible? He gave me an example of a simple pendulum and told that it is ...
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Why we can neglect rapidly oscillating terms in favor of slowly oscillating terms?

I never really understood why we can neglect rapidly oscillating terms in favor for slowly ones. As an example, in my quantum-mechanics studies I ran into this ODE: $$i\frac{d}{dt}\gamma_a = Ae^{i(\...
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Velocity of undamped pendulum [closed]

On this page, under the heading "Orbit Calculations": http://underactuated.mit.edu/pend.html or here. The author says, "This equation has a real solution when $\cos{\theta} > \cos{\theta_{\rm ...
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Why fields are solutions of waves equations?

This could be extremely trivial but I am having problems figuring it out. I think I understand properly the difference between waves and fields. A field is a function valued on space or spacetime ...
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Recommendations for good books on mechanical vibrations

I'm looking for books that explain/model vibration concepts such as multi degree of freedom vibrations from a mechanical vibrations standpoint (not waves). I'd prefer if it has proofs for most ...
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1answer
77 views

Do all even potentials produce periodic motion?

Consider a non-relativistic point particle of mass $m$ in 1D under the action of only conservative forces. Then by Newton's second law, the equation of motion is $$m\ddot{x}(t)=-U'(x(t)).$$ Now, do ...

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