Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

0
votes
1answer
29 views

Substituting into quantum harmonic oscillator

I'm a bit confused by the substitution that is often performed with the harmonic oscillator. This step is usually skipped over, but it has me a bit confused. I attached a picture to show what is ...
0
votes
1answer
29 views

Properties of Expectation Values Under Variable Substitution [on hold]

I am working on a homework problem from Griffiths QM (Problem 2.11, 3rd Edition). Specifically, I'm working on finding $\left<x^2\right>$ for the ground state and the first excited state of the ...
0
votes
0answers
18 views

What will be the kinetic energy expression in SHM with two bodies attached with spring?

I know Kinetic energy of two body system is $$KE = \frac{1}{2}\mu V^2_{rel}$$ where $\mu$ is the reduced mass $\mu = m_1 m_2 /(m_1+m_2)$ and Vrel is V1-V2 or the reverse .here I am not taking KE of ...
0
votes
0answers
17 views

Equation for Simple Harmonic Oscillator with moving base

It is known that the base of a simple harmonic oscillator moves according to a known function $u(t)$. Is the dynamics of this system given by $$m\ddot{x} = -\nabla V = -\nabla\frac{k}{2}|x - u(t)|^2 =...
-1
votes
1answer
26 views

Oscillating Bar on rollers [closed]

I'm currently preparing for my exam and am stuck at the following scenario. Suppose we have two rollers rotations against each other and now place a bar on top. The distance between the rollers is $L$...
2
votes
1answer
48 views

$N$ Independent Oscillators Entropy and Number of States

I have been working on building intuition and experience with solving problems related to the microcanonical ensemble, but I haven't been able to solve the following problem: If you have $N$ ...
0
votes
1answer
22 views

Effect of elasticity of string on simple pendulum

In a simple pendulum system, how does the extensibility/elasticity of the string affect the time period of oscillation? Would it lead to a random or systematic error? Would the elasticity of the ...
-2
votes
0answers
23 views

Finding the time value of a simple harmonic motion given positional equation [closed]

How do I find the $t$ value in $x(t) = 2.5\cos(\pi t)$ given that $x = 1.5$ My thought is that if I put: \begin{align} 1.5 &= 2.5 \cos(\pi t) \\ \cos^{-1}(1.5/2.5) &= \pi t \\ t &= \...
6
votes
3answers
128 views

Why does $\sqrt{\frac km}$ represent angular velocity and not frequency?

When I break down $\omega = \sqrt{\frac km}$ (angular velocity for a simple harmonic oscillator) into its units, I get: $$\omega = \sqrt{\frac{kg * \frac {m}{s^2}}{kg *m}}$$ which simplifies to: $$\...
0
votes
2answers
38 views

Does damping force depend on frame of reference?

I learn that damping force with regard to forced damped oscillations is given by F = -bv where is the velocity of the object measured from ground frame. Suppose we are in a frame which is moving with ...
4
votes
2answers
152 views

Why the time period of pendulum with infinite length is $84.6$ minutes? [closed]

In a book I was reading about SHM it stated: If the length of a simple pendulum is increased to such an extent that $\ell\to\infty$, then its time period is given by, $$T=2\pi\sqrt\frac{R}{g}\...
0
votes
1answer
54 views

Determine phase difference of harmonic oscillators

I am not understanding what I am doing wrong here. Please see the question below: Two harmonic oscillators are made using identical springs with identical masses and are set up side by side. You ...
1
vote
2answers
107 views

Does quantization go from quantum $\to$ classical or the other way around?

I was thinking about the relationship of classical mechanics to quantum mechanics, as I just took my first course in quantum mechanics. My specific question was about quantization. For a harmonic ...
0
votes
0answers
43 views

Why is a pendulum an example of harmonic motion?

I've heard a lot of people say that a pendulum moving back and forth on a fixed-length spring is an example of harmonic motion. But when I derive the governing equation for a pendulum, I get $$\theta'...
3
votes
1answer
42 views

Pendulum in a Boat [closed]

Suppose a pendulum is kept in a boat and it is oscillating. Now if the boat is made to oscillate in the same direction or opposite to that of the pendulum, how will these affect the amplitude of the ...
1
vote
1answer
41 views

Comparing measurements of a 2D quantum harmonic oscillator between cartesian and rotated cartesian coordinates

I've come across an old quantum exam problem that's causing me a bit of confusion, and I'm hoping someone can offer some clarity: There is a particle in a 2D harmonic oscillator potential such that ...
1
vote
1answer
37 views

How to calculate second-order correction to the energy from matrix elements of perturbation?

A particle is in the one dimensional harmonic potential $V(x)=\frac{1}{2}m\omega^2x^2$ with a small perturbation $V'$. I want to calculate the first- and second order correction to the ground state ...
1
vote
2answers
56 views

Making sense of phase portrait of simple mass-spring oscillator

I'm new to physics, and I'm having trouble making sense of phase portrait of the following system, $$ m \ddot{x} + k x = 0 $$ whose phase portrait is in here. Since $$ x(t) = \sqrt{\frac{2E}{k}} \...
2
votes
1answer
47 views

Is energy conserved in a Van der Pol oscillator?

The Van der Pol Oscillator is governed by a 2nd order ODE with nonlinear damping. The 'position' of the oscillator is the solution to $$x''(t) = \mu (1 - x^2(t)) x'(t) - x(t)$$ Here $\mu$ controls ...
0
votes
1answer
76 views

Difference between simple harmonic motion and angular SHM

I am not able to decipher when it is simple harmonic motion and when it is angular harmonic motion. Can we use both of them interchangeably? Can I know all the variable analogous for angular SHM (by ...
0
votes
1answer
24 views

Oscillations - Mass Change on Simple Pendulum

The problem that I am thinking of is phrased as follows: A person on a swing is holding a sandbag and is moving with some initial velocity $v_0$ at the bottom of the swing of length $l$. The ...
-1
votes
1answer
38 views

In the SHM equation $F= -kx$, $k =mw^2$ why not use $mf^2$ where $f$ is frequency $w$ here comes out to be $1/s$ not $\text{rad}/s$?

The reason I am stating this is because on calculating the units of w(omega) I found is equal to s^-1 not regular the rad/s. Proof: ...
-1
votes
1answer
41 views

Dependence of a pendulum's period on temperature

Does the time period of pendulum just increases with temperature or proportionately with temperature. If former is correct why latter is incorrect
0
votes
0answers
15 views

Calculating Amplitude of a block on an inclined surface

A block of mass 0.5kg which slides without friction on a 37 [degree] incline, is connected to the top of the incline by a massless spring of spring constant 120 N/m. Initially spring is stretched by a ...
14
votes
3answers
2k views

How does Ehrenfest's theorem apply to the quantum harmonic oscillator?

Ehrenfest's theorem, to my level of understanding, says that expectation values for quantum mechanical observables obey their Newtonian mechanics counterparts, which means that we can use newton's ...
-3
votes
1answer
60 views

Why do the units in the period of a mass-spring SHM not work out? [closed]

I am a high school physics teacher having students use the period of a mass-spring system with a known mass to determine the spring constant. We are practicing linearizing functions, so rather than ...
0
votes
0answers
40 views

Commutation in coupled Harmonic Oscillators

Starting with a coupled Harmonic Oscillator problem $$ H = \frac{p_1^2 + p_2^2}{2m} + \frac{K}{2}\left[x_1^2 + x_2^2 + \left(x_1 - x_2\right)^2\right] = \left(\frac{p_1^2}{2m} + \frac{2K}{2}x_1^2\...
0
votes
1answer
77 views

Schrodinger's Equation in three dimensions

Consider Schrödinger's Equation, $$H=\sum^3_{i=1} \frac{p^2_i}{2m_i}+V(x_1,x_2,x_3).$$ In one dimensional case, we can analyse the shape of the potential, i.e $$V(x)=\frac{1}{2}m_1 \omega^2_1 x^2$$ ...
0
votes
1answer
45 views

Why do we consider only one mass when solving linear harmonic oscillators in quantum physics?

While solving the Hamiltonian, books concentrate on the horizontal flow with only one mass attached to the string. Isn't there any consequences if we add more masses and why is friction always ignored?...
1
vote
1answer
30 views

Trouble following a chapter on harmonic oscillators (classical mechanics 5th edition)

I'm following Classical Mechanics, 5th Edition by Tom W.B. Kibble and Frank H. Berkshire. I'm following it since I'm interested in studying physics (although, am doing it at home myself). I've worked ...
1
vote
0answers
37 views

Does a 'Two block - spring ' system execute SHM under a permanent force? [closed]

When the following system is run , do the two masses execute oscillations while they are in motion , the kind we get when No permanent force is being applied like the one in this case , but a ...
-2
votes
2answers
104 views

Is a quantum harmonic oscillator always infinite dimensional?

Let us assume we have a quantum particle in a harmonic potential with the Hamiltonian $$H = \sum_n n \omega |n\rangle\langle n|$$ If I am not mistaken. Now when talking about harmonic oscillators ...
0
votes
0answers
48 views

Conceptual understanding of the Quantum Harmonic oscillator

First: When we consider a quantum particle in a harmonic (quadratic) potential we say that this particle is a harmonic oscillator, because it behaves like one. Is this correct? Now let us assume our ...
12
votes
4answers
2k views

Why can all solutions to the simple harmonic motion equation be written in terms of sines and cosines?

The defining property of SHM (simple harmonic motion) is that the force experienced at any value of displacement from the mean position is directly proportional to it and is directed towards the mean ...
0
votes
0answers
31 views

Invariant density of Harmonic oscillator

In general, dynamical systems described by a pure Hamiltonian can have an infinite number of invariant densities. In fact, each initial state determines exactly a closed path in phase-space and the ...
0
votes
3answers
80 views

harmonic oscillator position expectation value

I'm trying to get the expected value as a function of time for the position, of a harmonic oscillator hamiltonian and a state vector $|\psi\rangle=a|0\rangle+b|2\rangle$. I have $$|\psi(t)\rangle=...
0
votes
1answer
21 views

Determining stiffness of spring by dynamic method [closed]

I have been measuring stiffness of spring in physics lab by dynamic method. I made graph in MS Excel $\omega^2 =f (1/m)$ and than linear regression. I need to know, if in equation $y = kx + q$ the $k$ ...
1
vote
1answer
48 views

Physical understanding of the 'box' in quantum mechanics models [closed]

Few classic quantum mechanic models will be particle in a box (infinite depth), particle in a box (finite depth), harmonic oscillator (HO) and mechanical rotation (MR). The wave functions of a QM-HO ...
0
votes
1answer
70 views

Parity of Harmonic oscillator in 2 and 3 dimensions: the case of $l_z$

From doing exercises and trying to understand their solutions, i figured in two dimensions, not all values of $l_z$ can be taken by the particles (this is to conserve parity). For example, for n=0, ...
2
votes
2answers
135 views

Computation of $e^{i \hbar \omega a^{\dagger} a} a e^{-i \hbar \omega a^{\dagger} a}$

I need to compute terms like : $$e^{i \omega t a^{\dagger} a} a e^{-i \omega t a^{\dagger} a}$$ Where $[a,a^{\dagger}]=1$ (they are the bosonic annihilation/creation operators). I wonder if there ...
0
votes
2answers
27 views

What's the relation between acceleration, position and angular velocity?

I just encountered a problem involving lift and oscillations where I found the following differential equation: $$\ddot y = -\frac{ \rho gA}{m}y = -\omega^2 y$$ What's the relation between $\ddot y$, ...
1
vote
1answer
132 views

Is the quantum harmonic oscillator energy $E = n\hbar\omega$ or $E = (n + 1/2)\hbar\omega$? (Feynman Lectures)

Please, read the whole question. I've discussed a few contradictions and so far have not found an explanation for them. I was reading The Feynman Lectures on Physics (vol. 1), the part where he talks ...
0
votes
2answers
80 views

Approximating ground-state energy without using variational principle

Given the Hamiltonian for one dimension harmonic oscillator: $$H=-\frac{\hbar^2}{2\mu}\frac{d^2}{dx^2}+\frac{\mu\omega}{2}x^2 ,$$ I need to calculate the approximate ground state energy using the ...
0
votes
2answers
85 views

Several spring coupled: can such a movement happen or is it only theoretical?

We have 6 particles. We couple them 2 by 2 with a spring of strength $K$ (as in the picture below). We then have 3 harmonic oscillators. Then we couple each oscillator by a spring of strength $S\ll K$ ...
3
votes
4answers
283 views

Hamiltonian of quantum harmonic oscillator with $\psi(x)=\delta(x)$: comparison to classical mechanics

I was just reading the question Why can't $\psi(x)=\delta(x)$ in the case of a harmonic oscillator? The accepted answer says that $\psi(x)=\delta(x)$ is a mathematically valid state, though it's not ...
4
votes
1answer
162 views

Why can't $\psi(x) = \delta(x)$ in the case of Harmonic oscillator?

In the analysis of Harmonic Oscillator, it is claimed that $\langle\hat H\rangle$ cannot be zero, why is it so? I mean $\hat H = \frac{ \hat p^2 }{2m } + \frac12 k \hat x^2$, and $$\left<x^2\...
1
vote
2answers
33 views

Why does angular frequency of a particle in SHM does not change when it's velocity is changed

$V = A \omega \sin(\omega t + \theta)$ gives velocity of a particle in SHM at time $t$. But, why does the value of $\omega$ doesn't change when $V$ is changed?
0
votes
0answers
32 views

Volume within equi-energetic surface of a classical harmonic oscillator in microcanonical ensemble

$$ V(E) = \int_{H\leq E} d\mu = \int_\Gamma d\mu\, \Theta\bigl(E-H(q,p)\bigr) . $$ To compute the volume within the equinergetic surface in the microcanonical ensamble, we use the formula above, ...
0
votes
1answer
45 views

An equation for the simple harmonic motion

I know that this seems to be a pretty easy question but for some reason I can’t find any explanation for the following equation in any high school text book or on the internet. So according to my ...
0
votes
2answers
33 views

Damped drive oscillating systems

I am currently looking at the theory of find the viscosity of and object through damped harmonic motion, and tho it can be done there is obviously a limitation with regrades to the medium. If the ...