Questions tagged [harmonic-oscillator]

The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to an equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used to as toy problems that describe many physical systems.

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Pendulum on an accelerating train with changing length

Based on my own research, I found a general solution that can model a pendulum found on an accelerating train. F=-mgsin θ F≈-mgθ, applying small angle approximation F=-(mg/L) s, by applying arc length ...
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Does a tuning fork's resonance frequency increase with a repulsive force on it in AFM?

I have a tuning fork sensor with a probe tip that would be used in atomic force microscopy. Am I correct that the quartz tuning fork's resonance frequency increases with a repulsive force on it and ...
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Simple Harmonic Motion of a particle attached to a spring all inside a circle

I want to understand the following problem: The way I approached this question was using Hooke' Law. I managed to solve for $\lambda$ and later made a differential equation through which I got a ...
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Overlap between relative motion eigenbasis and single-particle eigenbasis in harmonic oscillator

The energy eigenstates of two particles in a 2d isotropic harmonic oscillator can be described in terms of a product basis of one particle states (I'm using the angular momentum basis with angular ...
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Along which axis is the moment of inertia of a harmonically oscillating body calculated?

I have been learning about oscillating bodies and recently stumbled upon physical pendulums. Now the problem is i don't understand about which axis is the MOI calculated while finding the TIME PERIOD(...
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How to calculate the damping ratio of a structure with a pendulum tuned mass damper?

I'm a highschool student investigating the damping of an oscillating structure by a pendulum mass damper. The structure has an accelerometer at the top to measure the acceleration. Although I know it ...
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Sidebands in spin-oscillator coupled devices

I am researching spin-oscillator hybrid devices (particularly those coupled to NV centers), and I have come across this paper investigating the strain field of a cantilever and its effect on the NV ...
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What is the velocity of the surface used to project the motion in this experiment for SHM? [closed]

What is the velocity with which the projection surface moves in this experiment?
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How to show that angular velocity is constant for a system that obeys Hooke's law- SHM for simple pendulum

How to show that angular velocity needs to be constant for an oscillating system to obey Hooke's law, in other words, that the system is in simple harmonic motion? I know that the system obeys Hooke's ...
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Showing a system is in Simple Harmonic Motion [closed]

A force of $F=(8-2x)$ is applied to a $2kg$ object in the $X$-direction. It is released from $6m$ away from the $x=0$ point. Show that the object is in a Simple Harmonic Motion. And derive a formula ...
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Double Pendulum and newtonian mechanics [duplicate]

I am searching for a way by which I can find the displacement vector of a double pendulum as functions of time.( without using lagrangian mechanics)
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Why does SHM happen in vacuum?

Very simply put, I don't understand why SHM happens. If a spring or a pendulum can attain lowest potential energy by stopping at the mean position, why don't both of them stop at the mean position ...
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Differential equations of a forced coupled spring-pendulum system

Currently working on a problem and I can really figure out how to write the differential equations for it. Here's the situation: So we have a mass $m$ tied to the wall with a spring of constant $k$. ...
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Density of state of a 2D harmonic oscillator

I tried to find the DOS of a 2D harmonic oscillator using $2$ different methods but the results aren't the same. The energy spectrum is: $$E_n=\hbar\omega(n+1)\tag{1}$$ and the degeneracy of the $n$-...
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How do I deduce the sign for the restoring forces in a system of N masses connected by N+1 springs?

Suppose we have a system of $N$ masses connected by $N+1$ springs, where the stiffness of the springs alternates between $k$ and $2k$. We assume N to be an even number. Determine the forms of the ...
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On the two different solution approaches of the quantum harmonic oscillator

The Hamiltonian for the harmonic oscillator (with $\hbar = m = 1$) is given by: $$\hat{H} = -\frac{1}{2}\frac{d^{2}}{dx^{2}} + \frac{1}{2}\omega^{2}x^{2}$$ This is assumed to be an operator on $\...
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Initial conditions of transient behavior of a driven oscillation

For a driven oscillation $$X_G = A_0e^{-\frac{\gamma}{2}t} cos(\omega_v t + \phi) + A cos(\omega_d t - \delta),$$ where $A_0$ and $\phi$ are determined by the initial conditions $x_0$ and $\dot x_0$ ...
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Is the square potential only modelled for an electron in an atomic bound state, and harmonic oscillator only for molecular states?

Quantum translational motions can be modeled with the particle in a box model and rotation and vibration can be modeled and harmonic oscillator models, respectively. Is the square potential only ...
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The mathemathical physics behind punching things that hang

How do you calculate the angle at which a hanging body will move when it is hit on it's hanging end?
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Difference between periodic motion vs harmonic motion vs simple harmonic motion

So , I am kind of confused about the difference between these three things: (i) Periodic motion. (ii) Harmonic motion. (iii) Simple harmonic motion It will be the best if someone showed me the ...
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Relationship between creation/anhilation and position/momentum operators

When solving the harmonic oscillator we introduce the creation/annihilation operator (ignoring constants) $$ a = \frac{1}{\sqrt{2}} \left(q + i p\right), \, a^\dagger = \frac{1}{\sqrt{2}} \left(q + i ...
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How can zero-point energy have any measurable effect when it is just a constant offset to the Hamiltonian?

In classical (say Hamiltonian) mechanics, adding a constant energy offset has no effect on the dynamics of the physical system. One way to understand this might be to understand that Hamilton's ...
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Waves and simple harmonic motion

Is it possible to always assume that a wave is generated from the medium components oscillating in simple harmonic motion with same amplitude but just out of phase with each other? For example, I've ...
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Resonance of a damped harmonic oscillator under forced oscillations

Suppose we have a damped harmonic oscillator and we also apply an external force such that our system oscillates in steady state. If the frequency of my force matches the natural frequency of my ...
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Power series of Hermite polynomial generating function [migrated]

The generating function for Hermite polynomials is: $e^{-s^2+2s\xi} = \sum_{n=0}^{\infty}H_n(\xi) \frac{s^n}{n!}$. How does one do the power series expansion for $e^{-s^2+2s\xi}$?
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How to picture the Quantum Harmonic Oscillator with particle creation interpretation?

For the simple quantum harmonic oscillator we can solve Schrodinger's equation and derive the analytic form of the eigenstates of e.g. a non relativistic electron in a harmonic potential. We may then ...
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Time for critically damped oscillator to reach equilibrium?

The title says it all. With my limited knowledge of physics and math, I have no idea where to begin, as the position function I have for a critically damped oscillator, $x=e^{-\omega_0t}[x_0+(v_0+\...
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Measuring the natural frequency of a spring-mass system with the graph

On a graph of a system under a external force y = distance and x = time where the external force start at t = 0, it's easy to find the driving frequency. $$F = \frac{\omega}{2\pi}, \omega = \frac{2\pi}...
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Harmonic motion: displacement

On my textbook the displacement in a simple harmonic motion is given as $$x = x(t)= A \cos(\omega t) \tag 1$$ It is true that $$x = x(t)= A \cos(\omega t)=A \sin(\pi/2-\omega t ) \tag 2$$ but why in ...
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A query about simple harmonic motion

Our teacher said that displacement $x = A \sin(\omega t)$ in simple harmonic motion and velocity $v = dx/dt = A\omega \cos(\omega t)$ or $A\omega \sin(\omega t + \pi/2)$. He also told us that $v$ ...
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Why do two pendulums with the same period meet at this angle?

"Two pendulums with the same mass and length $R$ are released from rest. The first pendulum is released from an angle of $\theta_1 = -2º$, and the second pendulum is released from an angle $\...
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Infinite wavelength for the 1D harmonic chain of oscillators corresponds to a uniform translation, but why does it still have a finite phase velocity?

The dispersion for the 1d chain of harmonic oscillators is $\nu = \sqrt{\frac{\alpha}{m}} \frac{|\sin(\pi k d)|}{\pi}$ Where I'm explicitly not using angular frequencies ($\nu = \frac{1}{T}, k = \frac{...
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Oscillator what's the steady state?

I'm wondering what's the steady state for an oscillator. Is it a system without driving force so without external force to disturb the system? If a system oscillates without driving force can we say ...
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How to find the max angle the pendulum reaches during oscillation?

I have a pendulum that is swinging with no loss of total energy. Is it possible to find out the maximum angle, $\:\theta_{o}$ to which the pendulum reaches, based on only the following information? ...
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Chameleon's tongue as a harmonic oscillator

I was watching a documentary about reptiles, at some point, it showed how chameleons catch their prey. Approximately, their tongue has an acceleration of $2500 \frac{m}{s^2}$, length of $0.7m$. They ...
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Period liquid in a U-tube [closed]

I have to find the oscillation period of a liquid inside a u-shapped tube. All I have is the density = $\rho$, liquid length = $l$ and the section = $A$ The only way I found is by the conservation of ...
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Forced Oscillation Explained with Violin String

In this lecture on Forced Oscillations, Normal Modes, Resonances, Musical Instruments, the professor says that by moving a bow over a violin string, you expose it to a lot of frequencies. Is there a ...
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Why is the tension equal to the spring force here?

Here the block is oscillating and to solve this question I took the tention in the string to be equal to the spring force But if that's the case a particle in the junction of the spring and the rope ...
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Why does a body in SHM have more probability (of being observed) at the extreme positions and not at other positions? [closed]

There is a question on the number of times a body comes to a place in a simple harmonic motion. Have a look: I thought that the answer was B because in each oscillation a body is at the extremes only ...
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Two spring-coupled mass system

I am confused with writing the equation of motion of masses and finding normal modes. The problems I've dealing with before, masses is always moved in same directions, and I determined if springs are ...
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A very interesting problem on simple harmonic motion and detailed analysis of momentum and energy involved

I am a high school student and I am a little confused in a question. this is a problem from Simple harmonic motion, I have found its solutions on many places but no solution turns out be convincing ...
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Quantum Harmonic Oscillator Virial theorem is not holding

I'm asked to calculate the average Kinetic and Potential Energies for a given state of a quantum harmonic oscillator. The state is: $$ \psi(x,0) = \left(\dfrac{4m\omega}{\pi\hbar}\right)^\frac{1}{4}e^{...
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Where do the constants in front of the analytical solution of the quantum harmonic oscillator come from?

I am going through Griffiths' Intro to QM, and in his solution the quantum harmonic oscillator, he just derived the recursion formula: $$a_{j+2}=\frac{-2(n-j)}{(j+1)(j+2)}$$ Using this, we can find ...
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Position operator and Momentum operator in the Energy basis

In studying Shankar quantum mechanics p.208 on expressing matrix elements of position operator and momentum operator in terms of the energy basis of the harmonic oscillator Hamiltonian $H=\frac{P^{2}}{...
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Will this system undergo simple harmonic motion? [closed]

I was recently studying Simple Harmonic Motion, In which I came across a problem. It deals with small angular oscillation (a light shaking of Sphere), I extended this problem and asked my teacher ...
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Why buckling is described by the maths of the harmonic oscillator?

Is this a coincidence or there is a more deep connection between the notion of the harmonic oscillator and the notion of buckling?
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How to determine the spring constant in a Lennard-Jones potential [closed]

I found the values of $u_1,u_2$ for 2 differents posistions ($r_1,r_2$) and I now have to determine the spring constant (k). I'm thinking about using $$F= -kx$$ with $F = -\frac{du}{dr}$ then $$U = \...
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Classical harmonic oscillator Green's functions

A recent paper (Modeling heat transport in crystals and glasses from a unified lattice-dynamical approach) derived expressions for thermal conductivity in a system of harmonic oscillators that decay ...
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Time Period of a damped physical oscillator [duplicate]

If I have a stick that is oscillating in air, and due to damping will its period increase or decrease? Damping will reduce its angular velocity as it opposes the motion of the stick, however, won't ...
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Can I use energy conservation to find out the new amplitude of SHM? [closed]

A mass $m_1$ connected to a horizontal spring performs S.H.M. with amplitude $A$. While mass $m_1$ is passing through its mean position another mass $m_2$ is placed on it so that both the masses move ...

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