Harmonic Definition and 1000 Threads

Homework Statement Derive the equilibrium state of a simple harmonic oscillation and show that the derivative of the maximum displacement is s^{'} = 2 \sqrt{E} Homework Equations F = -k x The Attempt at a Solution m a = -k s \rightarrow ms^{''}...

Homework Statement A spring is freely hanged on a ceiling. You attach a mass to the end of the spring and let the mass go. It falls down a distance of 49 cm and comes back to where it started. It contineous to oscillate in a simple harmonic motion going up and down - a total distance of 49...

Hi I am doing this completely out of self interest and it is not my homework to do this. I hope somebody can help me. Homework Statement In the book Biological Coherence and Response to External Stimuli Herbert Fröhlich wrote a chapter on Resonance Interaction. Where he considers the...

This thread will be dedicated for a trial to prove the following \sum_{k\geq 1} \frac{H^2_k}{k^2}=\frac{17}{4}\zeta(4)=\frac{17\pi^4}{360} \mbox{where }\,\,H^2_k =\left( 1+\frac{1}{2}+\frac{1}{3}+\cdots \frac{1}{k}\right)^2 In this paper the authors give solutions to the sum and others ...

Prove the following \sum_{k\geq 1} \frac{H^2_k}{k^2}=\frac{17}{4}\zeta(4)=\frac{17\pi^4}{360} \mbox{where }\,\,H^2_k =\left( 1+\frac{1}{2}+\frac{1}{3}+\cdots \frac{1}{k}\right)^2

Hello, Does the nth harmonic ALWAYS produce n loops, when referring to sound? If not, is there a general rule for this? Thanks.

Hello, When doing problems with SHM, my textbook says something like: An object in vertical shm is described by <insert some function>. Find the speed after X seconds. my question is, how do you know if the function is referring to the position of the object, or the velocity, or...

Homework Statement Please kindly help me. Actually I don't quite understand what the meaning of harmonic wave is and the mathematics that expresses it. h(x,y;t) = h sin(wt-kx+δ) h represents the position of the particle in a particular time? Or the wave motion? What is the physical...

The model of damped harmonic oscillator is given by the composite system with the hamiltonians ##H_S\equiv\hbar \omega_0 a^\dagger a##, ##H_R\equiv\sum_j\hbar\omega_jr_j^\dagger r_j##, and ##H_{SR}\equiv\sum_j\hbar(\kappa_j^*ar_j^\dagger+\kappa_ja^\dagger...

Homework Statement Considering the Hamiltonian for a harmonic oscillator: H=\frac{p^2}{2m}+\frac{mw^2}{2}q^2 We have seen that the equations of motion are significantly simplified using the canonical transformation defined by F_1(q,Q)=\frac{m}{2}wq^2cot(Q) Show explicitly that between both...

Homework Statement ## H=\frac{p^2}{2m}+\frac{1}{2}m\omega^2x^2## Show that ##[H,[H,x^2]]=(2\hbar\omega)^2x^2-\frac{4\hbar^2}{m}H## Homework Equations ##[x,p]=i\hbar## The Attempt at a Solution I get ##[H,x^2]=-\frac{i\hbar}{m}(px+xp)## what is easiest way to solve this problem?

I was reading through my Principles of Quantum Mechanics textbook and arrived at the section that discusses the quantum harmonic oscillator. In this discussion the equation ψ"-(y^2)ψ=0 presents itself and a solution is given as ψ=(y^m)*e^((-y^2)/2), similar to a gaussian function i assume. My...

The Hamiltonian is ##H=\hbar \omega (a^\dagger a+b^\dagger b)+\hbar\kappa(a^\dagger b+ab^\dagger)## with commutation relations ##[a,a^\dagger]=1 \hspace{1 mm} and \hspace{1 mm}[b,b^\dagger]=1##. I want to calculate the Heisenberg equations of motion for a and b. Beginning with ##\dot...

Homework Statement The velocity of an object in simple harmonic motion is given by v(t)= -(4.04m/s)sin(21.0t + 1.00π), where t is in seconds. What is the first time after t=0.00 s at which the velocity is -0.149m/s? Homework Equations N/A The Attempt at a Solution I thought this was...

This isn't homework. I'm reviewing calculus and basic physics after many years of neglect. I want to show that a damped harmonic oscillator in one dimension is nonconservative. Given F = -kx - \small\muv, if F were conservative then there would exist P(x) such that \small -\frac{dP}{dx} = F...

Hello everyone, looking around I have faith that the members of this forum will be able to point me in the right direction, and I apologize if it's more basic than I'm giving it credit for. I'm an experimental researcher in rock mechanics, but I've always been fascinated by elasto-dymamic...

Given a general solution to the fixed-end two-mass coupled harmonic oscillator(http://teacher.pas.rochester.edu/PHY235/LectureNotes/Chapter12/Chapter12.pdf), is there a set of initial conditions for position, velocity, the 3 spring constants, and 2 masses such that a transition from random phase...

Homework Statement Hey! I got this problem about 3D harmonic oscillator, here it goes: A particle can move in three dimensions in a harmonic oscillator potential ##V(x,y,z)=\frac{1}{2}m\omega^2(x^2+y^2+z^2)##. Determine the ground state wave function. Check by explicitly counting that it is...

Homework Statement The potential energy of a particle varies as U=K|X|3, it is oscillating and the amplitude is 'A' then find out the time period's variance with 'A' Homework Equations F=-dU/dx a=F/m The Attempt at a Solution none..

If the ladder operator ##a=\sqrt {\frac{m\omega}{2\hbar}}x+\frac{ip}{\sqrt{2m\hbar \omega}}## and ##a^\dagger=\sqrt {\frac{m\omega}{2\hbar}}x-\frac{ip}{\sqrt{2m\hbar \omega}}## then I get that the number operator N, defined as ##a^\dagger a## is worth ##\frac{m \omega...

Homework Statement Consider an electron confined by a 1 dimensional harmonic potential given by ## V(x) = \dfrac{1}{2} m \omega^2 x^2##. At time t=0 the electron is prepared in the state \Psi (x,0) = \dfrac{1}{\sqrt{2}} \psi_0 (x) + \dfrac{1}{\sqrt{2}} \psi_4 (x) with ## \psi_n (x) = \left(...

Homework Statement A simple pendulum is 5m long. What is the period of the oscillations for this pendulum in an elevator accelerating upwards at 5m/s2 and accelerating downards at 5m/s2Homework Equations ω = √(g/L) T = 2∏ / ωThe Attempt at a Solution I got the right answers (trial and...

Could hamiltonian of linear harmonic oscilator be written in the form? ##\hat{H}=\sum^{\infty}_{n=0}(n+\frac{1}{2})\hbar\omega |n\rangle \langle n| ##

Anyone know if there are any graphical simulations online for the field of a charged harmonic oscillator, or better yet maybe some kind of paper on it?

This feels silly asking but I have a question about units using the double harmonic approximation to determine IR spectral intensities. In the double harmonic approximation the intensity is given by the square of the derivative of the dipole with respect to a normal mode coordinate times a...

Homework Statement consider a harmonic oscillator of mass m and angular frequency ω, at time t=0 the state if this oscillator is given by |ψ(0)>=c1|Y0> + c2|Y1> where |Y1> , |Y2> states are the ground state and the first state respectively find the normalization condition for |ψ(0)> and the...

Homework Statement i need to calculate the orbital angular momentum for 3D isotropic harmonic oscillator is the first excited state The Attempt at a Solution for the first excited state...

Homework Statement I have a similar problem to this one on Physicsforum from a few years ago. Homework Equations Cleggy has finished part a) saying he gets the answer as Ψ(x, t) = (1/√2) (ψ1(x)exp(-3iwt/2+ iψ3(x)exp(-7iwt/2) OK classical angular frequency ω0 = √C/m for period of...

Homework Statement Okay, this one confuses me a bit: A particle is in a one-dimensional harmonic oscillator. At time t = 0 is given by its wave function ψ(x)=Nx3exp(-mωx2/2hbarred) a) At this point you measure the particle's energy. What measurement values ​​are available? Also...

Homework Statement I must calculate the probability that the position of a harmonic oscillator in the fundamental state has a greater value that the amplitude of a classical harmonic oscillator of the same energy.Homework Equations ##\psi _0 (x)=\left ( \frac{m \omega}{\pi h } \right ) ^{1/4}...

Homework Statement Calculate the expectation value for a harmonic oscillator in the ground state when operated on by the operator: $$AAAA\dagger A\dagger - AA\dagger A A\dagger + A\dagger A A A\dagger)$$ Homework Equations $$AA\dagger - A\dagger A = 1$$ I also know that an unequal number of...

Homework Statement The displacement of a particle along x-axis given by x=A sin^2(wt), where the symbols have their usual meaning. Is the particle motion simple harmonic? also find its time period. Homework Equations simple harmonic eqn iss of the form x=Asin(wt) or x=acos(wt)...

Homework Statement Homework Equations http://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_harmonic_oscillator The Attempt at a Solution Part a) I believe to find the mass I can use the equation $$ T = 2pi * sqrt( k / m ) $$ with T = 0.6s Part b) I am confused on...

Hi, I am reading through the book "Quantum Mechanics and Path Integrals" by Feynman and Hibbs and am having a bit of trouble with problem 3-12. The question is (all Planck constants are the reduced Planck constant and all integrals are from -infinity to infinity): The wavefunction for a...

Homework Statement I'm having some trouble calculating the 2nd order energy shift in a problem. I am given the pertubation: \hat{H}'=\alpha \hat{p}, where $\alpha$ is a constant, and \hat{p} is given by: p=i\sqrt{\frac{\hbar m\omega }{2}}\left( {{a}_{+}}-{{a}_{-}} \right), where {a}_{+} and...

Hi, I'm a bit of a newbie to additive synthesis.. I just want to clarify that I am doing the correct calculation before continuing. If I wanted to calculate the 5th harmonic of a square wave (the fundamental freq. being 200Hz and the amplitude of the fundamental being 1) would the...

Hello why we use cosine and sine in simple harmonic motion? why we use particularly cosine with potential energy and sine with kinetic energy of simple harmonic oscillator? regards

Homework Statement A uniform meter stick of mass M is pivoted on a hinge at one end and held horizontal by a spring with spring constant k attached at the other end. If the stick oscillates up and down slightly, what is its frequency? Homework Equations τ=rFsinθ f=(1/2π)√(k/m) F=kx...

Harmonic solutions as "Riemannian oscillators"? Has anyone heard of this idea before? Basically, you just solve the Schrodinger equation using n-dimensional spherical boundary conditions. Given n=2, you get what look like atomic orbitals. But rather than going the Born probalisitic route by...

1. The position of a mass oscillating on a spring is given by x=(.078m)cos[2∏t/(.68s)] when is the mass first at the position x=-.078m x=A cos(2πt/T). 3. the frequency is 1.47. I really don't know were to go from here. can anyone help me?

From page 91 of "Modern Quantum Mechanics, revised edition", by J. J. Sakurai. Some operators used below are, a = \sqrt{\frac{m \omega}{2 \hbar}} \left(x + \frac{ip}{m \omega} \right)\\ a^{\dagger} = \sqrt{\frac{m \omega}{2 \hbar}} \left(x - \frac{ip}{m \omega} \right)\\ N = a^{\dagger}...

Homework Statement A mass hanging from a spring is displaced and released so that it vibrates vertically. Its maximum height above a tabletop is 30 cm and its minimum height above the table top is 12 cm. The mass vibrates 20 times per minute. At time 0, its height is 30 cm...

I am currently working my way through Kitel's Solid State Physics book. When discussing the consequences of the harmonic assumption (quadratic degree of freedom for interatomic lattice interactions), he states that 1) the lattice waves do not interact 2) a single wave does not change form...

Homework Statement A particle with a mass of 65 g is moving with simple harmonic motion. At time t = 0, the particle is at its extreme positive displacement of 18.0 cm. The period of the motion is 0.600 s. Find the vecocity of the particle at t = 1.35 s Homework Equations (1). ω=2∏/T...

Question--- Angular Simple Harmonic motion.. Homework Statement A spherical ball of mass "m" and radius "r" rolls without slipping on a rough concave surface of large radius "R". It makes small oscillations about the lowest point. Find the time period of such oscillations. Homework...

Homework Statement A 0.241-kg particle undergoes simple harmonic motion along the horizontal x-axis between the points x1 = -0.349 m and x2 = 0.419 m. The period of oscillation is 0.511 s. Find the frequency, f, the equilibrium position, xeq, the amplitude, A. Homework Equations The...

Homework Statement A 0.500 kg mass is suspended from a spring and set into oscillatory motion. A motion detector is used to record the motion, and it is found that its velocity function is given by Vx(t) What are: a. the period of the motion; b. the amplitude; c. the maximum acceleration...

Homework Statement Hi guys, I don't really know how to solve the first part of a problem which goes like this: Consider a 1 dimensional harmonic oscillator of mass m, Hooke's constant k and angular frequency ##\omega = \sqrt{\frac{k}{m} }##. Remembering the classical solutions, solve the...

Hi guys, is there a reason why the energy of the harmonic oscillator is always written as:$$ E_{n} = \hbar \omega (n + \frac{1}{2})$$ instead of : $$ E_{n} = h \nu (n + \frac{1}{2})$$ ? THX Abby

In lecture, we are beginning to learn about waves and periodic motion under simple harmonic motion. We were given the equations: x=Acosθ and θ=ωt+\phi -- Substituting, we get x=Acos(ωt+\phi). This is simple enough; however what is Phi? All I was told is that "phi is a constant that allows us...