# Tagged Questions

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### Given the spring constant & maximum kinetic energy; length of spring extension? [on hold]

I need to understand the following question before i right my exam tomorrow. A body attached to a spring with spring constant 100 N/m executes simple harmonic motion. The maximum kinetiv energy of ...
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### How can I derive the Hamiltonian of simple harmonic oscillator from this Lagrangian?

I'm working through Leonard Susskind's Theoretical Minimum: Classical Mechanics and I can't seem to understand how the Hamiltonian of a simple harmonic oscillator is derived from the following ...
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### Derivation of $a_{j}$ coefficients in the quantum harmonic oscillator

In Griffiths' book page 53, when we derive the solution of the quantum harmonic oscillator by using the power series way, we have: $$a_{j+2} = \frac{2j+1-K}{(j+1)(j+2)}\, a_{j} .$$ And for large $j$, ...
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### Deriving spring oscilation period [duplicate]

We have a spring attached to a wall and at the other part an object on a frictionless surface. I tried to calculate the spring oscilation period. I used the conservation of energy and kinematics ...
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### Finding the minimum radius of the pivoted disc

Here is a question based on Simple Harmonic Motion that I tackled just now. However I think I am having an approach to tackle this but I am not sure about it. Ouestion: A uniform disc of radius ...
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### How can I find the motion equations of the 2-dim harmonic oscillator?

First of all: I am no physicist, so I am rather helpless. I need to find the moving equations of the 2-dim. harmonic oscillator. If it is possible it should be rather elementary, because, as I said, ...
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### Harmonic oscillator modified by infinite well: are analytic solutions possible?

I'm trying to find solutions to a harmonic oscillator that sits within an infinite square well. I haven't spent too much time yet, and I've had no success so far. I'm wondering how possible or complex ...
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### Spring problem? [closed]

I came across this problem in physics "Physics for Scientists and Engineers with Modern Physics by Serway" A block on the end of a spring is pulled to position $x = A$ and released from rest. In ...
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### Isotropic harmonic oscillator in polar versus cartesian

I read another Phys.SE post here: 3D Quantum harmonic oscillator that I believe says the wave function in Cartesian coordinates for a 3D harmonic oscillator is the product of the 3 one dimensional ...
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### Simple pendulum. quick question [closed]

I was trying to find an equation to find $T$ and $\omega$ for a simple pendulum when in an elevator while the elevator is accelerating. One scenario is when it accelerates in the positive up ...
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### How to find the phase constant? [closed]

I was given this velocity-vs-time graph of a particle in simple harmonic motion: I determined the amplitude to be $A = 1.15$ m, which Mastering Physics confirmed is correct. Then I was asked to ...
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### Equations of motion for a pendulum in 3D?

I am trying to solve for the equations of motion to simulate a pendulum. I decided to use the spherical coordinates. The Lagrange equation is: where L = length of the rope ϕ= angle of the ...
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### Ground State Wavefunction of Two Particles in a Harmonic Oscillator Potential

Question: Two identical, non-interacting spin-$1/2$ particles are in a 1D Harmonic Oscillator Potential. Their Hamiltonian is given by ...
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### Period of small oscillations [duplicate]

A light elastic string is stretched between two points, one lying vertically below the other. A particle is attached to the mid-point of the string, causing it to sink a distance h. Assuming that ...
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### Harmonic Oscillator Expectation Value

In Calculating the expectation value of the quantum harmonic oscillator, I've come across a problem for finding $\left \langle x \right \rangle$ for the coherent state $\left| \alpha \right \rangle$ ...
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### Mass-spring system on an incline

I am reviewing for an exam next week, and this is one of the questions I am stuck on. I have the mass-spring system above with spring constant $k$ on a frictionless incline. I would like to find the ...
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### The harmonic oscillator - ladder operators

Reading from Griffiths. I have got two questions. First, the halmiltonian operator that used to find the energy eigenvalue in only harmonic oscillator is: $$H={\hbar}w(a_-a_+-\frac{1}{2})$$ and ...
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### Is $\langle\psi_1|p\psi_1\rangle$ necessarily 0 for eigenstates? [closed]

Is $\langle\psi_1|p\psi_1\rangle$ necessarily 0 for harmonic oscillator eigenstates? If $\Psi(x,t)= c_0\psi_0(x)e^{-iE_0t/\hbar}+c_1\psi_1(x)e^{-iE_1t/\hbar}$, is the following true? Where $p$ is ...
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### Harmonic Motion [closed]

A light elastic string is stretched between two points, one lying vertically below the other. A particle is attached to the midpoint of the string, causing it to sink a distance h. Assuming that the ...
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### How To Use Ladder Operators?

I'm studying for a test in quantum mechanics and I'm having a hard time understanding how to use ladder operators. There are no examples in my text book, only definitions that I can't understand how ...
At a given instant of time, a harmonic oscillator undergoes a sudden change in spring constant from $k$ to $k'$. Show that for energy to be conserved in the accompanying transition, $\sqrt{k/k'}$ must ...