# 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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### Coherent state and continuous basis of Harmonic oscillator

While deriving the coherent states of the harmonic oscillator, I used a heuristic argument : Since $\hat{a}$ and $\hat{a^\dagger}$ form a continuous basis, and $[\hat{a},\hat{a^\dagger}] = 1$, we can ...
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### How to draw relation between Time Period and Amplitude of SHM?

Can we draw a relation between Time period and amplitude an object doing SHM? I came up with something but I’m not sure if it’s correct. $TA = k$, where k is a constant I came up with this just by ...
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### How will the movement of cart create an effect on time period of oscillation of ball? [closed]

In this question for finding the time period of bob I considered using the formula $T=2\pi\sqrt{\frac{l}{g}}$. It gives (d) option as one of the answer. My question is, will the movement of cart to ...
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### Why does resonance take place? [closed]

Resonance takes place when external driving frequency equals the natural frequency of an object. I know every objects have their natural frequency. But I can't see everything vibrating on its own, ...
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### Solution of a polynomial boson problem

I was reading about anharmonicity that can be added to the harmonic oscillator model and I got myself wondering whether it is possible and whether there is a general method to solve (I mean ...
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### Time spent by the bob of pendulum between two angles

Suppose we have a simple pendulum executing SHM about its mean position. We can easily notice that the bob of the pendulum swings back and forth making an angle, say $\theta$ about its central ...
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### Two masses connected by a spring

I have a question about a problem I saw on a website A mass is attached to one end of a spring, and the other end of the spring is attached to an immovable wall. The system oscillates with period T. ...
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### Is the drag coefficient the same thing as damping coefficient? Can I find the drag coefficient using the data of a damping oscillating sphere?

I am currently working on a lab experiment to find a relationship between the diameter of a sphere and its drag coefficient. I will be using a spring-mass system that oscillates vertically and then ...
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### Complex notation in harmonic oscillator

For a simple harmonic oscillator, $$x(t) = A \cos(\omega t)$$ We can also write $x(t)$ as: $$x(t) = C_1 e^{i\omega t} + C_2 e^{-i\omega t}$$ Why is it necessary that the coefficients $C_1$ and $C_2$ ...
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### Energy States of 2D Harmonic Oscillator with cross-terms in the potential

How can I find the energy of a particle in a 2D potential of form $V(x,y)= \frac{k}{2}(3x^2 + 3y^2 + xy + yx)$? It looks to have a close relation with Quantum Harmonic Oscillators, is it related to it?...
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### Computing ${\rm tr}\left[\hat{a}^{\dagger}\hat{a}\hat{D}(\alpha)\right]$

I'm having some trouble computing ${\rm tr}\left[\hat{a}^{\dagger}\hat{a}\hat{D}(\alpha)\right]$ where $\hat{D}(\alpha)$ is the displacement operator. I tried doing this using the number state basis, ...
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### Finding the drag coefficient of an object from damped simple harmonic motion (spring-mass system)

I am currently working on an experiment to determine the relationship between the diameter of a sphere and its coefficient of drag. I will be using a spring-mass system that oscillates vertically and ...
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### Mass hanging from vertical spring

Why does a mass hanging from an ideal spring, under gravity, undergo periodic oscillations? Isn't gravity a damping force here? Equation for mass spring system is given by $m\ddot{y}+ky=0$ where ...
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### How did Feynman derive the potential energy of the ballistic galvanometer?

In the Feynman Lectures Vol 1. Chapter 41 - The Brownian movement, the following statement is present under Section 1 - We know the formula for the kinetic energy of rotation—it is given by Eq. (19.8)...
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### Average energy of an SHM

Why do we usually calculate the average potential or kinetic energy of a simple harmonic motion with respect to time, why not with respect to position? Why even calculate average energy for an SHM? ...
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### Deriving the wavefunctions of coupled QHO without diagonalizing the Hamiltonian

I have the following Hamiltonian for two coupled quantum harmonic oscillators $$H=\frac{p_{x}^{2}}{2}+\frac{\omega^{2} x^{2}}{2}+\frac{p_{y}^{2}}{2}+\frac{\Omega^{2} y^{2}}{2}+\frac{C p_{x} y}{2}.$$ ...
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### Trouble following a chapter on harmonic oscillators (classical mechanics 5th edition)

I'm following Classical Mechanics, 5th Edition by Tom W.B. Kibble and Frank H. Berkshire. I'm following it since I'm interested in studying physics (although, am doing it at home myself). I've worked ...
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### Time period of a physical pendulum

Considering a physical pendulum consists of a thin homogeneous rod, is it possible to find the time period without calculating the moment of inertia of the rod?
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### Confusion on kinetic energy quadratic forms and eigenfrequencies

I am new to the idea of expressing kinetic energy in terms of the quadratic form. I noticed that online, people often express the kinetic energy as: $$T = \frac{1}{2} \dot q^T M \dot q \tag{1}$$ ...
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### Entanglement in 2D Harmonic Oscillator system

Let's assume a 2 dimensional harmonic oscillator system with the Hamiltonian $\hat{H} = \frac{1}{2} p_x^2 + \frac{1}{2} p_y^2 + \frac{1}{2} \omega_x^2 x^2 + \frac{1}{2} \omega_y^2 y^2$ with the ...
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### Does the brightness of day follow simple harmonic 'motion'?

Is it really true that the brightness during the day on earth follows simple harmonic motion? My teacher mentioned this as an example but it doesn't feel obvious to me by any stretch of the ...