# 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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### How would you go about scientifically comparing the physics of a game and real-life through gravity?

A bit of a hypothetical situation for y'all here. Let's say you want to test a video game's accurateness with regards to its physics; by seeing how closely the game's physics matches up with real-life ...
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### Direct Series Solution Attempt of the Quantum Harmonic Oscillator

The non relativistic Schrodinger equation of the harmonic oscillator in dimensionless variables is $$\frac{d^2 \Psi}{d \xi^2} = (\xi^2 - k)\Psi$$ where $$k \equiv \frac{2E}{\hbar \omega}$$ According ...
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### What is the single-mode quartic nonlinear oscillator evolution of a Fock state?

My question is how can I find the resultant state of for example Fock state $|n\rangle$ under single-mode quartic nonlinear oscillator evolution for time t? Attempt: I tried to find the relevant ...
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### What factors would cause a change in oscillation period as a result of a change in mass of pendulum bob?

I'm running an experiment in a video-game simulator (ish) called 'G-MOD'. I setup a typical pendulum setup, and measured the change in the period as a function of the pendulum's mass. I obviously ...
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### Slow parameter oscillations in coupled simple harmonic oscillator

In a paper by Turaev, he studies systems with a slow variation of parameters. The following is on page two, right column: He first discusses the one dimensional particle in a box, with ends at $x=-1$ ...
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### Transition probability between two harmonic oscillator states (Hemite polynomial integration)

Objective: Show that $$\int^{\infty}_{-\infty} x e^{-x^2} H_n(x) H_m(x) dx = \pi^{1/2} 2^{n-1} n! \delta_{m,n-1} + \pi^{1/2} 2^n (n+1)! \delta_{m,n+1}$$ My attempt at this is: \begin{eqnarray*} \...
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### Quantum Mechanics: Harmonic Oscillator - Evaluating the expectation value to obtain the generating function for the moments [closed]

I don't know how to start evaluating the expression. I keep ending up with a messy integrand. Please help.
We have a mass sustained by a spring $K$ and a damper $C$, with a base excitation. Let's call $s(t)$ the base excitation and $x(t)$ the mass motion. The differential equation of this system will be: $... 1answer 40 views ### Does maximum velocity change when vertical mass-spring system is used in different location on Earth in SHM? Let me elaborate for you my concerning I am thinking of a example of a vertical mass spring system. Suppose i place my system at equator, let suppose a wall clock which uses a vertical spring mass ... 2answers 23 views ### Is gravitational Force is damping force in vertical mass-spring system of constant k in Simple Harmonic motion When a block of mass m is suspended by vertical spring system,it for sure perform SHM in the absence of damping force,only force which act on the system is internal which is -kx, where k is spring ... 3answers 33 views ### What is the differnce of angular velocity and angular frequency in angular SHM A body free to rotate about a given axis can make angular oscillation. This angular oscillation are called Angular simple harmonic motion, In derivation, Ohm = theta ✖ w ✖ cos(wt+ phi) Where omega is ... 0answers 63 views ### Is there a physical process that - ignoring measurement uncertainties - has a fixed duration? I'm looking for a process that has an absolutely fixed duration, where all the variance obtained by measurement is just due to measurement uncertainty, and the obtained mean is the actual duration of ... 0answers 26 views ### Understanding difference between classical and quantum harmonic oscillator probability distributions Here we have an example QHO wavefunction squared in blue overlayed an equivalent CHO probability distribution. I'm trying to understand intuitively why the QHO result has zeros, i.e. points where we ... 1answer 59 views ### Damped harmonic Oscillator Lagrangian equivalence The objective is to prove that the Lagrangian: $$L'=\frac{2\dot x+\lambda x}{2\Omega x}\tan^{-1}(\frac{2\dot x+\lambda x}{2\Omega x})-\frac{1}{2}\ln(\dot x^2+\lambda \dot{x } x + \omega^2x^2), \qquad \... 3answers 37 views ### How can we be sure that the equation of SHM that works for one dimension of an object moving in circular motion works for all SHM? I have learned that a component of a uniform circular motion is an example of SHM. And I have no question about it, I totally understand that. I also understand how we can derive formulas like \vec{... 2answers 52 views ### The Negative Energy in the Harmonic Oscillator Potential! [closed] I'm self studying Quantum mechanics from Griffiths. Now I'm at the Harmonic oscillator potential. All my questions raised after defining the ladder operators a_- and a_+. If \psi satisfies the ... 1answer 333 views ### Why probability density for simple harmonic oscillator is higher at ends than that in middle? I was watching this crash course by Geek Lesson on Quantum Mechanics specifically for Quantum Harmonic Oscillator and [at 1:54:54] when video shows the plot of probability density for different states ... 1answer 48 views ### Direction of displacement Displacement is defined as the vector obtained by joining the final position to the initial position (head towards the final position). Well,i know this is silly but what are these final and initial ... 2answers 22 views ### Can the heating of the spring in oscillator be modeled by a velocity dependent force? In a damped oscillator, the damping term is represented by a velocity dependent force b \ \dot{x}. This makes sense if the damping is due to viscosity of the medium. Is this modeling correct for the ... 2answers 39 views ### The position and potential energy of the masses in two mass rigid body pendulum lie on a cirlce Suppose I have two mass rigid pendulum, both of whose masses are equidistant from the pivot point at P. All three points lie on a circle of diamater D and subtend an angle \alpha at the pivot. let ... 0answers 23 views ### How does time translational invariance and linearity imply exponential solutions? I'm currently studying "Waves and Oscillation". While going through the book The Physics of waves, from page 11-12. The author has mentioned that the differential equation being linear ... 0answers 38 views ### The quantisation of the harmonic oscillator applied to the free Klein-Gordon field In David Tong's lecture notes on quantum field theory, at the bottom of page 23, we are applying the quantisation of the harmonic oscillator to the field to obtain expressions for the field operators ... 1answer 45 views ### Quantum Harmonic Oscillator and an instantaneous force that imparts a momentum The question is as follows, Consider a simple harmonic oscillator in its ground state. An instantaneous force imparts momentum p_0 to the system. What is the probability that the system will stay in ... 2answers 45 views ### Simple harmonic motion problem I have no problem with the solution provided but, I have a problem with understanding it's meaning. Shouldn't the two solutions for b) add up to be the period? If not, why? 2answers 46 views ### Speed of a standing wave Standing waves are the waves in which disturbances do not simply propagate forward or backward, but rather the material particles are moving up and down continuously, with the particles between two ... 1answer 63 views ### Question about a relativisticaly accelerated harmonic oscillator How can the speed of oscillation of a harmonic oscillator be affected if somehow it got accelerated to a relativistic speed perpendicular to its oscillation? Can this be compared with the effect on ... 2answers 80 views ### Solutions to damped harmonic oscillator? For the damped harmonic oscillator equation$$\frac{d^2x}{dt^2}+\frac{c}{m}\frac{dx}{dt}+\frac{k}{m}x=0$$we get that the general solution is$$x(t)=Ae^{-\gamma t}e^{i\omega_d t}+Be^{-\gamma t}e^{-i\... 1answer 33 views ### Resonance and standing waves on a bar [closed] I'm having trouble solving this problem: By applying a harmonic force, acting on the end of a free bar of length$L$, a standing wave is formed due to multiple reflections: Where are the nodes of ... 1answer 35 views ### A spring with non-negligible mass I see everywhere in the analysis of a spring-mass system of Simple Harmonic Motion, that each infinitesimal element on the spring of length$L$is$\frac{vx}{L}$where$v$is the velocity of the block ... 0answers 12 views ### What does the disconuity in the equation for modulated phase mean when superposing two SHM? So I was working out the result of the composition of two SHM that are in the same direction and have different frequencies and amplitudes. Turns out I found the following equation for the modulated ... 2answers 42 views ### Is displacement related to velocity or mass (in this question)? [closed] Two blocks of masses$m_{1}$and$m_{2}$are kept on a smooth horizontal surface. A spring of mass$m$and natural length$L$connects the two blocks as shown in the figure. At t=0,$m_1$and$m_{2}$... 1answer 33 views ### Energy transfer between oscillators [closed] Suppose I have two mechanical oscillators$a(t), b(t)$, coupled through the interaction$V_\text{int} = \mu^2 a(t) b(t)$. Is there a simple way to express the rate of energy transfer from$a$to$b$... 0answers 33 views ### Does the uncertainty$\Delta \hat a\$ of the annihilation operator of the harmonic oscillator remain constant over time?
I'm supposed to prove that the uncertainty of the annihilation operator of the harmonic oscillator, given by $$\Delta \hat a=\sqrt{\langle\hat{a}^{2}\rangle-\langle\hat{a}\rangle^{2}} \tag1$$ doesn't ...