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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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I need to find the drag coefficient of a pendulum bob

Is it possible to find the drag coefficient of a pendulum bob from the damping caused on it during swinging. I will be able to measure its displacement from the point of origin and plot it against ...
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Exact equation of exponential curves of underdamped harmonic motion

I was studying the underdamped harmonic motion and got curious about the fact that the decreasing exponentials $\pm Ae^{-\gamma t}$ are good approximations only for light damping $(\gamma<<\...
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Transition amplitudes

We have a forced simple harmonic oscillator Lagrangian $$L = \frac{\dot{\phi}^2}{2} - \frac{m^2{\phi}^2}{2} + f(t)\phi \, .$$ The external force goes to $0$ as $t \to \pm \infty$. I'm trying to ...
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Amplitude of a Reflected wave on a joined strings with different linear densities

There are two strings with different linear densities joined together end to end and placed under tension. As an example, If the amplitude of the wave incident on the boundary from the first string ...
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Calculating the time taken for a oscillator to get to a specific point? [on hold]

There is a simple harmonic oscillator with a mass of 0.5 kg, and a spring constant of 10 N/m and an amplitude of 0.03 m. How do I find at what time does the oscillator get to x=-0.01 m position if ...
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How do we know which term to attach a phase factor to in a state equation?

I need to find the state of a particle in a one-dimesional harmonic oscillator where a measurement of the energy yields the values $\hbar\omega\over 2$ or $3\omega\hbar\over 2$, each with a ...
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Why does the position uncertainty of a harmonic oscillator not have the expectation value squared term?

My question is about the derivation for the uncertainty of a quantum harmonic oscillator in the non-zero ground state energy. In my textbook A modern Approach to Quantum Mechanics by John S. Townsend ...
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Why is the number of excited vibrational modes $g(\nu)d\nu$ proportional to $x^2e^{-x}$ in Debye's theory?

I come across a problem in Terrell Hill's "Introduction to statistical thermodynamics" saying that: In the Debye theory, the number of excited vibrational modes in the frequency range $\nu$ to $\nu+...
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Angular SHM and center of mass

This has been confusing me for a while. Consider a solid, homogeneous rod of mass $m$ and length $l$, hanging from a fixed pivot. Its center of mass is located at $\frac{1}{2} l$, and its moment of ...
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Computing the excited states of the harmonic oscillator [closed]

I have a question about solving a wavefunction in the second, fifth, sixth excited states and the use of Hermite polynomials. The general formula for a normalized eigenfunction: $$ \Psi = \sqrt{\frac{...
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Numerically Modeling Coupled Oscillators Point Masses

I seek to model the motion of two coupled oscillating point masses as shown below: Note that x1(t) models the leftmost point mass and x2(t) is the motion of the rightmost point mass. I would like to ...
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What is the difference between solutions to 2nd order homogeneous ODE?

I’m studying Vibrations, and we have two forms to the 2nd order homogeneous ODE: $$mx ̈+kx ̇=0$$ $$x(t)=C_1 e^{iw_n t}+C_2 e^{-iw_n t}$$ and $$x(t)=A\cos(w_n t)+B\sin(w_n t)$$ Even though I can use ...
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What is meant by finite harmonic oscillator?

What does it mean to take finite harmonic oscillator, In research article "http://iopscience.iop.org/article/10.1088/1367-2630/17/11/113015 ", we were finding effective number of cobosons in ...
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Why does an object in simple harmonic motion have kinetic energy at its equilibrium point? [closed]

While an object is undergoing simple harmonic motion, its kinetic energy tends to vary with its position. This kinetic energy is highest when it's at the point where the forces on it are at ...
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If $\psi$ acting on $a_+$ and $a_-$ operator just moves up and down the ladder, why is $[a_-, a_+] = 1$ and not 0? [duplicate]

If $\psi$ is acted upon by both the operators one by one, it should return the same wave function. Thus order in which you increase or decrease the energy shouldn't matter. Then why is it so that the ...
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cushioned harmonic oscillator problem with the inicial phase

my problem is how to discover the phase ($\phi$) of the cushioned harmonic oscillator $$ x(t)=A e^{\frac{-\gamma t}{2}}cos(\omega t+\phi) $$ I have as my initial conditions $$ \begin{cases} x_o(t=...
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Volume in first octant

Here we are finding number of state less than energy E for particle trapped in 3D harmonic potential .For large value of E as compare to hw , we assumed energy levels as continuous.And we introduces ...
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Why are there two different averages for the kinetic energy in a harmonic oscillator?

Question: A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is? ...
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Harmonic Oscillator and Shifts in Derivative Operators

What symmetries/symmetry breaking arises from shifts in the derivative operators? To explain what I mean let's study an example. The classical one particle one dimensional harmonic oscillator has the ...
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Computing Green function using Wick rotation

Consider the SHO with a Lagrangian given by $ L = \frac{1}{2} (\hat{p}^2-m^2\hat{x}^2) $ The Green function is defined as $ G(t)= \langle0|T \hat{x}(t)\hat{x}(0)|0\rangle $.Where $T$ is the time ...
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The creation and annihilation operators in quantum mechanics

What is the result of the commutation relation between the creation operator and a power of the annihilation operators in simple harmonic oscillator problem?
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Quantum Harmonic Oscillator propagator in Sakurai

In Sakurai the derivation of the propagator leads to the expression $$u_n(x)\exp{\left(\frac{-iE_nt}{\hbar}\right)} = \left(\frac{1}{2^{n/2}\sqrt{n!}}\right) \left(\frac{m\omega}{\pi\hbar}\right)^{1/...
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Is critical damping same as resonance condition?

Because frequency of external force is equal to that of the natural frequency of oscillator...can we call it resonance condition...if yes or no why? If no,then when do we get resonance?
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Linear combination of eigenstates in a potential [closed]

Linear combination of a set of vectors is only defined for a finite set of vectors even though the set might be an infinite set. In quantum mechanics we take infinite linear combination of all ...
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Motion along length of a spring [closed]

What's relation between velocity of each part of a massive spring undergoing Simple Harmonic Motion.
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What is a complex phase shift?

In a complex methods course I am taking, we were given an equation for a particular driven harmonic oscillator where the driving force is trigonometric. I have worked out the math and obtained an ...
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Is the harmonic oscillator approximation valid in occasion of very powerful fields?

I noted that in physics, to study electromagnetic wave phenomena when there is a sinusoidal behaviour, often is used the approximation of harmonic oscillation. I tried to understand the basics of why ...
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Degeneracy of anisotropic oscillator

I was working on the 3D isotropic harmonic oscillator and I found that the energies are given by: $$E=\hbar\omega(n_x+n_y+n_z+3/2)$$ Which has a degeneracy of $\tfrac12(n+1)(n+2)$. However, when ...
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Which equation to use for SHM?

Usually every simple harmonic question starts with the line: The block at equilibrium shifted to a position $X_0$ and released. I found this from the website: https://study.com/academy/lesson/...
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Large Damped Harmonic Oscillator misunderstanding

So I'm confused, here with what is highlighted. When the book says of "order $1/y_-$" you will reduce the displacement by a factor of $1/e$. Does of order mean when the time is equal to $1/y_-$, if ...
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How LC oscillator is used for generating signals?

I have been trying to understand some practical applications of LC oscialltors and I dont seem to find much information available on net. One consistent application that I see is "LC circuits are used ...
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Why is the restoring force not zero at the equilibrium position of simple harmonic motion?

The restoring force is applied in order to take the body it's equilibrium. Then in a SHM why in the mean position restoring force maximum rather than being zero as it has reached equilibrium. (After ...
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$\sqrt{-1}$ coefficient in a function

In a simple harmonic oscillator with $\ddot{x} = -\omega^2x$, it can be shown through differentiation that one solution can be given by $\dot{x} = i \omega Ae^{i \omega t}$. What does the factor of $i$...
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Tension in pendulum [closed]

I am asked to calculate the tension in the rope of a pendulum at (a) its initial position as well as at (b) its lowest position. $L = 3 m$ $α = 10^o$ $mass = 2kg$ (a) For the intial point I used ...
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Bose-Einstein condensation in 1D harmonic oscillator and its density of states

I have troubles understanding how (and whether) Bose-Einstein condensation works in 1-D harmonic oscillator. From my calculation it seems that in limit of infinite number of particles, almost all of ...
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Does “the initial phase of oscillation is 45°” mean a time dependence of the form $\sin(\omega t+\pi/4)$ or $\cos(\omega t+\pi/4)$? [closed]

A point particle of mass 0.1 kg is executing SHM with an amplitude 0.1 m. When the particle passes through the mean position, its kinetic energy is $8 \times 10^{-3}$ Joule. Obtain the equation of ...
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Rod connected to springs. Can this oscillate if the rod has no mass?

My thoughts led me to change the question's title. Here's what I've tried in solving the problem and led me to ask the question in the title. We have the following diagram where the beam has no mass ...
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Equation of motion from potential energy [closed]

Given that the potential energy of a particle in 2D space is $$V(x, y) = \frac{1}{2}k(x^2 + y^2),$$ find the equations of motion and show they are circular orbits. Substituting $r^2 = x^2 + y^2$, I ...
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How to derive this expression for the free scalar field in QFT? (Peskin & Schroeder)

In the introductory text to quantum field theory by Peskin & Schroeder, they state that in analogy to the simple harmonic oscillator in quantum mechanics, the free scalar field can be expressed as:...
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Why does $g$ show up in the frequency of this oscillation?

The problem diagram is given in the picture below: Having looked at this question Why does the acceleration $g$ due to gravity not affect the period of a vertically mounted spring? something troubles ...
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Physical meaning of commutation

I was reading the solution to quantum harmonic oscillator by J.J. Sakurai. He uses the annihilation and creation operators and there's a key step (I think) which is $$[a,a^{\dagger}]=1$$ I know we can ...
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Simple harmonic motion with pulley with mass

The problem is presented in the following diagram I'm refreshing things I've already learnt and I know I have some major gaps but I've searched and haven't managed to find a similar problem. The axis ...
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2answers
71 views

A harmoinic oscillator in the Heisenberg picture

Considering the Hamiltonian of a harmonic oscillator \begin{equation} H=\frac{p^2}{2m}+\frac{m\omega^2 x^2}{2}, \end{equation} the time evolution of the Heisenberg picture position and momentum ...
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Energy level in harmonic oscillator [duplicate]

ground state is always non degenrate in harmonic oscillator in quantum state, why?
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Is there a proof for why the acceleration of an object undergoing simple harmonic motion related to angular velocity squared?

Many textbook says the defining equation of the acceleration of an object undergoing simple harmonic motion is $$a= -\omega^2 \times x.$$ Is there a reason as to why acceleration is related to $\...
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A particle is in a harmonic oscillator potential. Which are the possible spreads for a simultaneous measurement of the momentum? [closed]

A particle is in a harmonic oscillator potential, not in the ground state. The position of the particle is known with an rms spread of $1\mathring{\text{A}}$. Which of the following are possible ...
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understanding lock-in measurements (XY display mode)

I am trying to understand the lock in measurement performed here. Mainly, I am trying to understand how they were able to choose the phase offset based on the plot (first image below). In the ...
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1answer
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What is the effect of mass on resonance amplitude?

When a system is undergoing forced oscillations, why does reducing the mass of the system cause the frequency response curve to shift downwards? I encountered this problem in a practice paper, but I ...
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1answer
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Using a single harmonic oscillator to implement a quantum gate. Confusion over concept

I'm trying to simulate a quantum gate operation in mathematica using a harmonic oscillator and I have some confusion with how the physical system relates to the theory. This may be a bit long winded ...
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Can anyone explain the harmonic oscillator (in context to quantum mechanics) 2.3 (Griffiths) using Taylor series?

At the end he concludes $V(x) = V''(x_0)(x-x_0)^2$. How does he get to know that the rest are $0$? How does he conclude $V''(x_0) = k$. Please try to explain in easy ways and tough vocabulary. I don't ...