Harmonic Definition and 1000 Threads

The figure below shows a system in equillibrium. The pulley and the springs (both with constants "k") are ideal. The period of oscillation of the mass A is given by: Relevant equations: F = -kx (SHM) I tried to do a "force diagram" and set up some geometric relations but it´s not working.

Are quantum harmonic oscillators, vacuum fluctuations and radiation modes the same? Is vacuum energy caused by vacuum quantum fluctuations?

Problem: A pendulum that has a period of 3.00000s and that is located where the accleration due to gravity is 9.79 m/s^2 is moved to a location where the acceleration due to gravity is 9.82 m/s^2. What is its new period, in s? Equations Equation for Harmonic motion: x = A sin (2pi * f * t)...

Homework Statement Hi everybody! In my quantum mechanics introductory course we were given an exercise about the 3D quantum harmonic oscillator. We are supposed to write the state ##l=2##, ##m=2## with energy ##E=\frac{7}{2}\hbar \omega## as a linear combination of Cartesian states...

Homework Statement Consider a two-dimensional harmonic oscillator, described by the Hamiltonian ##\hat H_0 = \hbar \omega (\hat a_x \hat a_x ^{\dagger} + \hat a_y \hat a_y^{\dagger} + 1)## Calculate ##\hat H_0 \hat L | n_1, n_2 \rangle## and ##\hat L \hat H_0 |n_1, n_2 \rangle##. What does...

I'm studying the motion of a physical pendulum, could someone help me make the final step in figuring out how to find the period so I can make predictions before carrying out a practical? Basically I have a meter rule with holes drilled along the length and will be pivoting it at various points...

Homework Statement If a mass attached to a spring has motion given by the equation X(t) = 5(sin(3pi(t))), what is the equation for the acceleration of the spring? What is the angular speed of the spring,and what is its frequency and period? If the spring has a spring constant of 900 N/m, what...

Homework Statement I am having issues with d) and would like to know if I did the a, b, and c correctly. I have tried to look online for explanation but with no success. A harmonic oscillator executes motion according to the equation x=(12.4cm)cos( (34.4 rad /s)t+ π/5 ) . a) Determine the...

Homework Statement The acceleration amplitude of a damped harmonic oscillator is given by $$A_{acc}(\omega) = \frac{QF_o}{m} \frac{\omega}{\omega _o} \sqrt{\it{R}(\omega)}$$ Show that as ##\lim_{\omega\to\infty}, A_{acc}(\omega) = \frac{F_o}{m}## Homework Equations $$\it{R}(\omega) =...

Homework Statement A simple harmonic oscillator has a potential energy V=1/2 kx^2. An additional potential term V = ax is added then, a) It is SHM with decreased frequency around a shifted equilibrium b) Motion is no longer SHM c)It is SHM with decreased frequency around a shifted equilibrium...

There's a pendulum attached to a car accelerating with ##A##. I know I can find it's time period using the "effective" g method, but I want to find it from first principles. My attempt: ##tan\theta = A/g## Now I displace it by ##\alpha## giving ##mgsin(\theta+\alpha)-mAcos(\theta+\alpha) = ma##...

Homework Statement The question is uploaded. The Attempt at a Solution I have completed the whole question, however, stuck on the last part. How to find the value about which ## \rm \small \theta## now oscillates? A source stated that ## \rm \small \alpha## is the value about which ## \rm...

I am basically just rewriting a question that was posted on other forums. While watching videos of a MIT lecture on the eigenstates of angular momentum (video: '16. Eigenstates of the Angular Momentum II' by MIT OpenCourseWare) the professor visualized different spherical harmonics for low...

Why is it that the fundamental harmonic is louder than rest? If energy is the same as frequency surely the greater the harmonic the louder it is. Also what does amplitude represent in waves?

Homework Statement [/B] Estimate the total harmonic distortion [THD] present in the current waveform using the formula: Homework Equations ##THD\left(I\right)=\frac{1}{I1}\sqrt{\sum_{n=2}^\max\left(In\right)^2}\times 100\%## The Attempt at a Solution I have attached a worksheet for this. The...

Homework Statement Solve the damped harmonic motion system \ddot{x} + 2k\dot{x} + \omega^2 x = 0 with initial conditions \dot{x}=V at x = 0 in the cases (i) \, \omega^2 = 10k^2 (ii) \omega^2 = k^2 (iii) \omega^2 = 5, k = 3 Identify the type of damping, sketch the curve of x versus t>0 in...

Homework Statement the velocity of a harmonic wave in a strung-wire is 1550m/s and the wave's frequency is 740Hz there are two oscillators (?) in the wave called A and B such that B is 2m further ahead of A in the direction of the wave's travela) calculate the phase difference between A and B...

Homework Statement What is the value of ## \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + ... ## ? Homework Equations [/B] I have no idea since it's neither a geometric nor arithmatic seriesThe Attempt at a Solution [/B] My Calculus purcell book tells me that it is e - 1 ≈...

Not sure if this is the best place to ask this question but forums on this seem to be limited, can anybody explain how one would discover if a steel pole lighting structure is being effected by harmonic resonance? I do not know what tools and methods would be used, if anyone can provide some...

Homework Statement Find the first-order corrections to energy and the wavefunction, for a 1D harmonic oscillator which is linearly perturbed by ##H'=ax##. Homework Equations First-order correction to the energy is given by, ##E^{(1)}=\langle n|H'|n\rangle##, while first-order correction to the...

Hello! I'm looking for books (or webpages, anything is welcome) with exercises dealing with methods applied to the harmonic oscillator, especially creation and annihilation operators, coherent states, squeezed states, minimum uncertainty states, Fock states, displacement operators... I have...

Homework Statement Calculate the partition function, the entropy and the heat capacity of a system of N independent harmonic oscillators, with hamiltonian ##H = \sum_1^n(p_i^2+\omega^2q_i^2)## Homework Equations ##Z = \sum_E e^{-E/kT}## The Attempt at a Solution I am not really sure what to...

Homework Statement Hello all, I have a question regarding the damping constant for a model of a vertically oscillating mass on a spring. I have read through one or two similar questions on this site but I think I can manage to be a little more specific about what I'm asking. I am in a physics...

Homework Statement Substitute \psi = Ne^{-ax^2} into the position-space energy eigenvalue equation and determine the value of the constant a that makes this function an eigenfunction. What is the corresponding energy eigenvalue? Homework Equations \frac{-\hbar^2}{2m}...

Hello, I'm studying the section 2.2 of "Introduction to Quantum Mechanics, 2nd edition" (Griffiths), and he shows this equation $$\frac{\partial^2\psi}{\partial x^2} = -k^2\psi , $$ where psi is a function only of x (this equation was derivated from the time-independent Schrödinger equation) and...

Okay, so I have just started with simple harmonic motion(SHM). So the equation of displacement in my textbook is given as: X= ACos(wt +x) where A is the amplitude X is displacememt from mean position at time t w is angular frequency x is phase constant...

Homework Statement String A is stretched between two clamps separated by distance L. String B, with the same linear density and under the same tension as string A. String B is stretched between two clamps separated by distance 4L. Consider the first eight harmonics of string B. For which of...

Homework Statement [/B] What is the shortest time required for a harmonic oscillator to move from ##x = A## to ##x = \frac{A}{2}##? Express your answer in terms of the period ##T##. Homework Equations [/B] ##x(t)=Acos(\omega t)=Acos(2\pi\frac{t}{T})## The Attempt at a Solution ##A=Acos(0)##...

Homework Statement I got an alpha particle (charge 2+) fixed at x=0 and an electron fixed at x=2. I then add a fluor ion (charge 1-) to the right of the electron and we note his position xeq. The question is to find the constant spring (k) relative to the harmonic oscillation made by the fluor...

Homework Statement An equation of motion for a pendulum: (-g/L)sinΦ = Φ(double dot) Homework Equations L = length g = gravity ω = angular velocity Φο = initial Φ The Attempt at a Solution The solution is Φ=Asinωt+Bcosωt solving for A and B by setting Φ and Φ(dot) equal to zero respectively...

Homework Statement For the first half of a trip a car has velocity v1; for the second half of a trip it has velocity v2. What is the mean velocity of the car? (The book does not mention a direction.) Homework Equations Arithmetic mean: $$\frac{v_{1}+v_{2}}{2}$$ Harmonic mean...

Homework Statement a mass is placed on a loose spring and connected to the ceiling. the spring is connected to the floor in t=0 the wire is cut a. find the equation of the motion b. solve the equation under the initial conditions due to the question Homework Equations ## \sum F=ma ## ##...

Homework Statement An object of mass m = 300g is attached to a spring with a constant k = 3.0Nm-1 and is at rest on a smooth horizontal floor in a fluid where the resistive force is assumed to be linearly proportional to the velocity v. the object is then displaced 10mm to the right of the...

Homework Statement A particle of mass 10g is placed in potential field given by V= (50x^2+100)erg/g. what will be the frequency of oscillation? Homework Equations n(frequency)=2pi(K/m)^1/2 The Attempt at a Solution F= -dU/dx . given is potential field. so dU/dx= (2*50x +0)=-100x. equating it...

Homework Statement A spherical ball of mass “m”, moment of inertia “I” about any axis through its center, and radius “a”, rolls without slipping and without dissipation on a horizontal turntable (of radius “r”) describe the balls motion in terms of (x,y) for a function of time. **The...

Homework Statement http://imgur.com/a/FDfAp What is the phase constant? Homework Equations x(t) = A*cos(ωt+Φ) The Attempt at a Solution If I'm not mistaken at t = 0 the graph starts at half the amplitude or 5. Also the amplitude of this graph is 10, and at t = 0 angular velocity is also 0. 5...

Homework Statement A damped harmonic oscillator consists of a block (m = 2.72 kg), a spring (k = 10.3 N/m), and a damping force (F = -bv). Initially, it oscillates with an amplitude of 28.5 cm; because of the damping, the amplitude falls to 0.721 of the initial value at the completion of 7...

Homework Statement A very light, rigid rod with a length of 0.620m extends straight out from one end of a meter stick. The stick is suspended from a pivot at the far end of the rod and is set into oscillation. (a)Determine the period of oscillation. (b)By what percentage does this differ from...

The ladder operators of a simple harmonic oscillator which obey $$[H,a^{\dagger}]=\hbar\omega\ a^{\dagger}$$. --- I would like to see a proof of the relation $$\exp(-iHt)\exp(a^{\dagger})\exp(iHt)|0\rangle=\exp(a^{\dagger}e^{-i\omega t})|0\rangle\exp(i\omega t/2).$$ Thoughts?

Homework Statement Show the mean position and momentum of a particle in a QHO in the state ψγ to be: <x> = sqrt(2ħ/mω) Re(γ) <p> = sqrt (2ħmω) Im(γ) Homework Equations ##\psi_{\gamma} (x) = Dexp((-\frac{mw(x-<x>)^2}{2\hbar})+\frac{i<p>(x-<x>)}{ħ})##The Attempt at a Solution I put ψγ into...

The pattern above will continue for all values of the harmonic sequence. Will a destination point be reached for any value of θ where 0 ≤ θ < 2𝜋? (I know it won’t for θ = 0) Is there a function which contains the set of all destination points?

If there is a length thread with a metal ball attached at the end of the thread, and there is a oscilliation. The restoring force is F=mgsinθ, my question is can we consider this as a centripetal force and link it to this equation: mv^2/r.

How do you find the wave function Φα when given the Hamiltonian, and the equation: aΦα(x) = αΦα(x) Where I know the operator a = 1/21/2((x/(ħ/mω)1/2) + i(p/(mħω)1/2)) And the Hamiltonian, (p2/2m) + (mω2x2)/2 And α is a complex parameter. I obviously don't want someone to do this question...

Homework Statement A cheerleader waves her pom-pom in SHM with an amplitude of 17.3 cm and a frequency of 0.830 Hz . Find the maximum magnitude of the velocity.Homework Equations v = -w Asin(ωt+Φ) = -wx or Conservation of Energy: 1/2kx2 + 1/2mv2 = 1/2kA2 The Attempt at a Solution I tried v =...

Homework Statement A 1.10 kg mass on a spring has displacement as a function of time given by the equation x(t)=(7.40cm)cos[(4.16rad/s)t−2.42rad]. Find the position of the mass at t=1.00s; Homework Equations x = Acos(ωt+∅) The Attempt at a Solution I tried to just plug in the time t in that...

I have been thinking of this and can not seem to understand why nonlinear loads can be tought of harmonic current sources injecting current back into the grid? For example if you connect a passive filter in parallel to attenuate the 5th harmonic, the 5th harmonic would flow between the filter...

Imagine that you have plucked a string and it is vibrating as a standing wave at its fundamental tone (frequency f1). You leave it there and later on come back with the intention of bringing it up to the second tone (frequency f2). What should you do? It seems obvious: apply a stimulous...

Suppose u(x,y) and v(x,y) are harmonic on G and c is an element of R. Prove u(x,y) + cv(x,y) is also harmonic. I tried using the Laplace Equation of Uxx+Uyy=0 I have: du/dx=Ux d^2u/dx^2=Uxx du/dy=Uy d^2u/dy^2=Uyy dv/dx=cVx d^2v/dx^2=cVxx dv/dy=cVy d^2v/dy^2=cVyy I'm not really sure how to...

Homework Statement ...when she pulls the ball down 2.5cm from equilibrium and releases it from rest, it oscillates at 5.5 Hz. What is displacement y as functions of t? Homework Equations Y= Acos(omega t+phi) The Attempt at a Solution I'm almost certain I should instead be using sin to...

Homework Statement How to calculate the matrix elements of the quantum harmonic oscillator Hamiltonian with perturbation to potential of -2cos(\pi x) The attempt at a solution H=H_o +H' so H=\frac{p^2}{2m}+\frac{1}{2} m \omega x^2-2cos(\pi x) I know how to find the matrix of the normal...