# Tagged Questions

The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to a 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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### Damped Oscillations: Incoherence between a general solution and a specific one

In my 'Classical Dynamics of Particles and Systems, THORNTON/MARION, 5th Edition' book of classical mechanics it is given the following general solution for a damped oscillation solving ...
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### What is the physical meaning of $a_{\vec{p}} \! \mid \! 0 \rangle$

$a^\dagger_{\vec{p}} \! \mid \! 0 \rangle = \mid \! p \rangle$ is interpreted as a creation of a particle with momentum $p$ from the vacuum. $a_{\vec{p}} \! \mid \! p \rangle = \mid \! 0 \rangle$ is ...
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### The period of a mass-spring system including a pulley [closed]

A spring with spring constant $k$ is attached to a mass $m$ as illustrated in the following four set ups: Calculate the period of the motion for each of them. In cases (1) and (2) the period ...
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### Why is $\pi$ used when calculating the value of $g$ in pendulum motion?

I am trying to intuitively understand why $\pi$ is used when calculating the value of $g$ using the harmonic motion of a pendulum: $$g ~=~\frac{4\pi^2L}{T^2}.$$ Does it have something to do with the ...
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### Driven-damped oscillator: deduce the phase and/or resonant freq from amplitudes at varying freqs

Suppose that we have a fairly standard driven-damped harmonic oscillator (i.e. linear spring restoring force, linear damping force, sinusoidal driving force, etc). The catch is: we don't know the ...
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### What could be the applications of Damped Oscillation? [closed]

I've been researching on Damped Oscillation for a few days for a research paper, however I couldn't find any of its applications on the web, though there are few examples of it, but they couldn't be ...
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### A driven quantum harmonic oscillator (DQHO) [closed]

I'm trying to find the dispersion relation for the DQHO with Lagrangian $$L(q,\dot q,t)=\frac{1}{2}\dot{q}^2-\frac{1}{2}\omega q^2+F(t)q$$ with $F(t)$ being non-zero for $0<t<T$. The ...
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### What is the significance of clamping the center of the spring?

7. A block is hung on a spring, and the frequency $f$ of the oscillation of the system is measured. The block, a second identical block, and the spring are carried in the Space Shuttle to space. ...
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### Damped simple harmonic oscillator problem

I'm supposed to calculate and draw the phase space trajectory for this: for the two different cases when and . I've never done this sort of question before, how are they done? I've tried ...
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### Sums of operators in practice

Consider a one dimensional harmonic oscillator. We have: $$\hat{n} = \hat{a}^{\dagger} \hat{a} = \frac{m \omega}{2 \hbar} \hat{x}^2 + \frac{1}{2 \hbar m \omega} \hat{p}^2 - \frac{1}{2}$$ And: ...
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