Harmonic Definition and 1000 Threads

Homework Statement I am trying to follow Sakurai's use of perturbation theory on a harmonic oscillator, Homework Equations Perturbation: v=\epsilon x^2 , \epsilon << 1 Matrix elements: V_{km}=<k|v|m> The Attempt at a Solution The book says that all other matrix elements besides V_{00}...

Homework Statement I solved this physics question, but I am unclear about why Amplitude was the amount the spring was stretched by (which should be the new equilibrium point), instead of the amount the person pulled the mass down by (which should be the amplitude). Can anyone help? On your...

Homework Statement http://imagizer.imageshack.us/v2/275x215q90/661/kIVMcC.png Mathematical pendulum is the part of the oscillating circuit. The system is in a constant uniform magnetic field. Oscillations is small. Find the normal modes of oscilations. Homework Equations ## \begin{cases}...

Homework Statement A simple pendulum of length =30.0cm is released from rest from an angle of θ=10.0∘ to the vertical. Assuming that the pendulum undergoes simple harmonic motion, find its maximum speed. Source: https://isaacphysics.org/questions/accuracy_shm_pendulum_num Homework Equations a)...

Homework Statement A mass on the end of a spring is released from rest at position x0. The experiment is repeated, but now with the system immersed in a fluid that causes the motion to be critically damped. Show that the maximum speed of the mass in the first case is e times the maximum speed...

Homework Statement Explain the shape of the velocity-displacement and acceleration-displacement graphs for an object undergoing simple harmonic motion. The graph is attached to this thread Homework Equations v = wsqrt(A^2-x^2) where w = angular frequency, A = amplitude and x = displacement...

Homework Statement A particle of mass m in the harmonic oscillator potential V(x) = (mω2x2)/2 is described at time t = 0 by the wavefunction χ(x, t = 0) = 1/[(2πσ2)1/4] exp[-x2/(4σ2)] What is <E> at time t? Homework EquationsThe Attempt at a Solution <T>+<V>= <E> I've found the expectation...

Homework Statement Question: "The midpoint of a guitar string oscillates with an amplitude of 2.24mm with a frequency of 400Hz. Calculate: i) The maximum speed at this point ii) The maximum acceleration of the string at this point" Homework Equations Suitable formulas: x=Asin(2*pi*f*t) ...

For example, I have a pendulum with amplitude of 2m, when the pendulum is at a displacement of 2m, wouldn't the acceleration be negative as the restoring force is acting towards equilibrium? The equation I am taught is that maximum acceleration is (2*pi*frequency)^2 * amplitude, which is a...

Hey PF. This isn't a homework question and I'm hoping this is the right place to ask it, sorry if it isn't! In the case of a weakly damped harmonic oscillator driven by a sinusoidal force of the form Fe^(iwt). The form of the differential force equation of motion is then given by ma + cv +kx =...

I have the following homework problem that I am having trouble with. Any guidance would be appreciated. Thank you in advance. Consider an object hanging on a spring, immersed in a cup of water. The water exerts a linear viscous force -bv on the object, where v is the speed of the object...

Hi people! Today I was doing some QFT homework and in one of them they ask me to calculate the Harmonic Oscillator propagator, which, as you may know is: W(q_2,t_2 ; q_1,t_1) = \sqrt{\frac{m\omega}{2\pi i \hbar \sin \omega (t_2-t_1)}} \times \exp \left(\frac{im\omega}{2\hbar \sin \omega...

I've been trying to prove a rather simple looking concept. I have a code that calculates states of a 3D anisotropic oscillator in spherical coordinates. The spherical harmonics basis used to expand it's solutions in radial coordinate constraint the spectrum such that when the Hamiltonian is...

Hi all, I'm in a intro to wave phenomenon class this semester and unfortunately, our textbook is written by the professor and is really not very good at all. So I'm liking for any recommendations on D.E. books that do well with explaining harmonics. Any recommendations would be greatly appreciated!

1. A platform is executing simple harmonic motion in a vertical direction with an amplitude of 5 cm and a frequency of 10/pi vibrations per second. a block is placed on the platform at the lowest point of its path. a) at what point will the block leave the platform? b)how far will the block...

Homework Statement I am trying to derive the formula for simple harmonic motion of a mass hanging on a spring. I understand the derivation for the situation when the mass and the spring are on an horizontal table. Then I go about deriving the same formula for the situation when a mass is...

Homework Statement A 100kg bungee jumper attached to a bungee cord jumps off a bridge. The bungee cord stretches and the man reaches the lowest spot in his descent before beginning to rise. The force of the stretched bungee cord can be approximated using Hooke's law, where the value of the...

I was wondering if we can somehow use the formula Potential Energy = 1/2K(x(x=Amplitude))^2 for a pendulum if we are only given the angle of displacement? Would the problems normally just say the PE at the top of the pendulum is such and such, please find max Velocity, Or also the max...

I have learned in 1st year that the under-damped simple harmonic motion can be described by the differential equation m \frac {d^2 x} {dt^2} + b \frac {dx} {dt} + kx = 0 where m is the mass, b is the constant of linear drag and k is the spring constant But the derivation is skipped...

This isn't homework. I'm reviewing physics after many years of neglect. Since a simple harmonic oscillator is a conservative system with no energy losses, then a driven undamped harmonic oscillator, once the transient solution has died out, can't be receiving any energy from the driving...

Is the propagation of a wave simple harmonic motion? Simple harmonic motion is defined when the restoring force is proportional to the displacement. Hooke's Law F = -kx is an example. However at my level of understanding I have not yet read about the relationship between forces and waves and...

Homework Statement A harmonic oscillator of mass m and angular frequency ω experiences the potential: V(x) = 1/2mω^{2}x^{2} between -infinity < x < +infinity and solving the schrodinger equation for this potential yields the energy levels E_n = (n + 1/2)...

Homework Statement The spin 1/2 electrons are placed in a one-dimensional harmonic oscillator potential of angular frequency ω. If a measurement of $$S_z$$ of the system returns $$\hbar$$. What is the smallest possible energy of the system? Homework Equations...

Homework Statement The Hamiltonian for the 3-D harmonic oscillator in spherical polar coordinates is given in the question.The question then asks : using the trial wavefunction ##ψ=e^(-αr) ## show that Homework Equations ##<ψ|H|ψ>/<ψ|ψ> = (\hbarα)^2/2m + 3mω^2/2α^2## The following...

(I am referring to section 3.1 in Burkhardt's "Foundations of Quantum Physics", if you happen to have the book.) In that book it's pointed out that the apparent contradiction between the pdf's of the QM ground state solution to the harmoinc oscillator with its classical conterpart (at the...

Homework Statement Hi all! I'm slightly confused about pendulums and simple harmonic motion. In my textbook, it says that a pendulum only exhibits simple harmonic motion when the angle is small (<10 degrees). I was wondering why this is, using equations if possible. Without the math, I think...

Homework Statement Consider a particle of mass m in a harmonic potential: If the particle is in the first excited state (n = 1), what is the probability of finding the particle in the classically excluded region? Homework Equations The Attempt at a Solution I sub in...

Hello Forum, The 1D harmonic oscillator is an important model of a system that oscillates periodically and sinusoidally about its equilibrium position. The restoring force is linear. There is only one mode with one single frequency omega_0 (which is the resonant frequency). What about the...

Dear kind helpers, actually I am not 100% sure whether this is the right place to post, as it is not a homework in the sense of an exercise sheet. But I think it could be because it feels pretty basic and that I should be able to solve it. Though I really searched for a solution but could not...

if we have two non-interacting particles of mass M in a one-dimensional harmonic oscillator potential of frequency ω, with the wavefunction defined as: $$\Psi\left(x_1,x_2\right) = \psi_n\left(x_1\right) \psi_m\left(x_2\right)$$ where x_1 and x_2 are two particle co-ordinates. and ψ_n is the...

Homework Statement The e-functions for n=0,1,2 e-energies are given as psi_0 = 1/(pi^1/4 * x0^1/2)*e^(x^2/(2*x0^2) psi_1 =... psi_2 =... The factor x0 is instantaneously changed to y= x0/2. This means the initial wavefunction does not change. Find the expansions coefficients of the...

[SIZE="4"]Definition/Summary An object (typically a "mass on a spring") which has a position (or the appropriate generalization of position) which varies sinusoidally in time. [SIZE="4"]Equations x(t)=A\sin(\omega t)+B\cos(\omega t) \omega^2 =\frac{k}{m} [SIZE="4"]Extended...

[SIZE="4"]Definition/Summary This is the quantum-mechanical version of the classical harmonic oscillator. Like the classical one, the quantum harmonic oscillator appears in several places, and it also appears in the quantization of fields. This article will discuss the one-dimensional...

I feel I understand what happens, and how to solve the equation of motion x(t) for a mass attached to a spring and released from rest horizontally on a smooth surface. We typically end up with x(t) = x_0 cos(ωt) as the solution, with x_0 as the amplitude of the oscillation. But I've...

Homework Statement A two-dimensional isotropic harmonic oscillator of mass μ has an energy of 2hω. It experiments a perturbation V = xy. What are its energies and eigenkets to first order? Homework Equations The energy operator / Hamiltonian: H = -h²/2μ(Px² + Py²) + μω(x² + y²) The...

why simple harmonic motion is projected as or compared with uniform circular motion ?

I have a homework problem where I have to solve for the displacements of the attached system using cyclic symmetry. To do this, I know that I have to find the harmonic load components of the system. One thing that my professor did not make clear (or if he did, I missed it) is how to determine...

in defining the Equation of simple harmonic motion taking origin as fixed point and the line of motion as x axis. a(acceleration) = - w^2 * x. where w^2 is positive constant. what is the reason behind taking square of w as constant not just w?

I am working through Leonard Susskinds 'the theoretical minimum' and one of the exercises is to show that H=ω/2(p^2+q^2). The given equations are H=1/2mq(dot)^2 + k/2q^2, mq(dot)=p and ω^2=k/m. q is a generalisation of the space variable x, and (dot) is the time derivative if this helps...

Homework Statement Find the expectation values of x and p for the state \vert \alpha \rangle = e^{-\frac{1}{2}\vert\alpha\vert^2}exp(\alpha a^{\dagger})\vert 0 \rangle, where ##a## is the destruction operator. Homework Equations Destruction and creation operators ##a=Ax+Bp##...

A particle of mass is connected to a spring with a force constant K. The particle undergoes simple harmonic with an amp A. What is the potential energy of the partic when the position is (1/2A)? Homework Equations E=1/2kA^2 1/2kdelta^2=1/2mv^2+1/2kx^2 The Attempt at a Solution...

Homework Statement A block on a horizontal surface is attached to two springs whose other ends are fixed to walls. A light string attached to one side of the block initially lies straight across the surface. The other end of the string is free to move. There is significant friction between...

Homework Statement I was told that for an object to execute SHM, the x (distance displaced from the spring) can't be greater than e . Why is this so? i can't understand. can someone explain please? Homework Equations The Attempt at a Solution

Homework Statement For a particle of charge ##q## in a potential ##\frac{1}{2}m\omega^2x^2##, the wavefunction of ground state is given as ##\phi_0 = \left( \frac{m\omega }{\pi \hbar} \right)^{\frac{1}{4}} exp \left( -\frac{m\omega}{2\hbar} x^2 \right)##. Now an external electric field ##E##...

Homework Statement Homework Equations The Attempt at a Solution I find this task very hard to understand. First of all, when adding more mass, wouldn't that change the acceleration, according to F=ma? And in that case the velocity should also change when adding more mass, shouldn't it? That...

Homework Statement A wheel with moment of inertia I. A mass of M is connected to a belt and runs over the wheel with radius R and connected to a spring with a stiffness of k which is connected to the ground. Show that if the mass is pulled down with a force of F and released the system will...

Homework Statement my question is on part d, (iv), i assume this is a pendulum experiment. the equlibrium position is at 30cm. then the negative amplitude should be located at 24.0cm. the particle moved from 24.0cm to 36.0cm. the acceleration is always acted towards the equlibrium position. so...

Homework Statement Find harmonic conjugate of u(x,y)=ln(x^2+y^2) and specify the region it is defined then show u has no harm conj on C\{0} Homework Equations The Attempt at a Solution Ok so i found the harmonic conj by converting to polar and found it to be v(r,Θ) = Θ. I am...

Hello I was given this problem, and I have two possible answers and I really just need someone to verify which one is right, or at least in the right direction. Thanks! Homework Statement A cart is floating on an airtrack and is connected by a spring to one fixed object. The cart executes...