# 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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### Three dimensional isotropic harmonic oscilator Hamiltonian

Let us consider the Hamiltonian for the isotropic three dimensional harmonic oscilator: $$H = \dfrac{\mathbf{P}^2}{2m}+\dfrac{m\omega^2\mathbf{R}^2}{2},$$ where $\mathbf{P}$ and $\mathbf{R}$ are the ...
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### Free particle and harmonic oscillator coupled

I'm currently playing with a toy model given by the Lagrangian $$L=\frac{m\dot{x}^2}{2}+\frac{m\dot{y}^2}{2}+\frac{1}{2}m\omega^2x^2+x y,$$ which is basically a free particle (described by $y(t)$) and ...
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### Variation of the effective spring constant of a trampoline-like arrangement of springs with diameter

I'm currently investigating the simple harmonic motion of the following system of springs: The second diagram represents the center mass executing simple harmonic motion up and down about the ...
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### Resonant frequency(s) of system of resonant objects?

I am trying to gain a better understanding of resonance when we are dealing with a coupled system of resonating objects. For example, say we have a single gas bubble in liquid and suppose it ...
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### Simple harmonic motion in a horizontally accelerating lift [duplicate]

How would the time period of a pendulum in a lift be if the lift was accelerating horizontally to the right ? My teacher did it by putting a pseudo force "ma" to the left, then getting the resultant ...
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### Period on the phase plane (small oscillations)

I have this formula to calculate the period of a motion in the phase space (plan, in this case) along a phase curve. $$T(E)=\int_{x_1}^{x_2}\frac{dx}{\sqrt{2(E-U(x))}}$$ ...