# 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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### If friction is not proportional to velocity, why do we model it as such when considering damped oscillations? [duplicate]

Early in our study of mechanics, we learn that friction is usually proportional only to normal force, without dependence on velocity. However, during our studies of damped oscillations, we often model ...
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### Why does $x_0V''(x_0)$, i.e. the constant force term of the $-V''(x_0)(x-x_0)$ term of a Taylor expansion, have no effect on the equation of motion? [closed]

My waves and vibrations class suggests that $F(x)\approx-V''(x_0)(x-x_0)$ is equivalent to $F(x)\approx-V''(x_0)x$ when considering only oscillations about the equilibrium position; i.e. that the term ...
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### Why am I getting this derivation of time period of pendulum in an accelerated frame wrong? [closed]

We are working in the frame of the cart and we are trying to obtain the $\tau=k\theta$ form. So, let's write the $\tau=I_{axis}\alpha$ first for a small deviation $\theta$ from the vartical. (The ...
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### Potentials increasing faster than harmonic oscillator

I'm reading a book which says: (HO stands for harmonic oscillator): The spectrum of the HO has equidistant energy eigenvalues. A potential that increases quicker than the HO has states which become ...
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### Spherical quantum oscillator: Is energy smaller than the potential?

A particle with mass $m$ is inside the spherical quantum well $V(r)$: V(r)= \begin{cases} -V_0, & \text{if}\ r<a \\ 0, & \text{otherwise} \end{cases} \...
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### Understanding the dynamics of a perturbed quantum harmonic oscillator system

I'm trying to understand how quantum systems behave when they are perturbed, and I'm using the quantum harmonic oscillator as a model. I start by implementing a symmetric gaussian shaped bump in the ...
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### Plot of Number of Oscillations of a Pendulum

I have been studying the oscillations of a ball attached to a string which is released from some initial angle $\theta$. The number of complete oscillations over a certain time interval $\Delta t$ is ...
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### Can we equate SHM with motion in a circle?

So in SHM, $v = r\omega\cos\omega t$. But we also know that $v = r\omega$ from circular motion. Then, we can write $$r\omega = r\omega\cos \omega t$$ $$1 = \cos\omega t \tag{1} \label{1}$$ 0 = \...
Consider the lagrangian of a system of classical coupled harmonic oscillators of mass $M$, connected with springs with elastic constant $\chi$ and connected to the background with springs of elastic ...