Harmonic Definition and 1000 Threads

HI! I was wandering if there is a proof that the harmonic sum \sum\frac{1}{k} has no closed form. Something like the proof that an equation with degree more than 4 has no solution in terms of radicals.

Hi, why does the harmonic plane wave have the form below: V(r,t)= acos[\omega (t-\frac{r\cdot s}{v})+\delta ] (r is the position vector, s is the vector that points to the direction the wave is propagating, v is the wave propagation velocity and delta is the phase constant).

Homework Statement Let Sn = 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}...+\frac{1}{n}. Show that |S2n-Sn|\geq \frac{1}{2} Homework Equations The Attempt at a Solution So I'm going to try and use induction Base case let n=1 |S2n-Sn| = \frac{1}{2} So true for base case...

Hi,I am Vikas Joshi and I'm studying last year Electronics Engineering. I am doing project on Harmonics Monitoring using Micro-controllers. I have some doubts about it.They are as follows: 1.How to detect Harmonics from Single Phase supply.What kind of circuits I should use to detect specific...

When people talk about harmonic oscillators it seems to me that they always assume either that the relationship of force and displacement is linear, or that it behaves in some sinusoidal fashion. Do you always have to assume one to be able to arrive at the other? Or is there something I'm...

Homework Statement particle experiencing SHM with frequency f= 10 hz find the displacement x at any time t for the following initial conditions. @ t=0 x=0.25m v=0.1 m/sHomework Equations x=Asin(ωt+∅) v=Aωcos(ωt+∅)The Attempt at a Solution So with frequency I find ω which then is subbed into...

Find under what conditions the transformation from (x,p) to (Q,P) is canonical when the transformation equations are: Q = ap/x , P=bx2 And apply the transformation to the harmonic oscillator. I did the first part and found a = -1/2b I am unsure about the next part tho: We have the...

Homework Statement A 3D harmonic oscillator has the following potential: V(x,y,z) = \frac{1}{2}m( \varpi_{x}^2x^2 + \varpi_{y}^2y^2 + \varpi_{z}^2z^2) Find the energy eigenstates and energy eigenvalues for this system. The Attempt at a Solution I found the energy eigenvalue to...

I was reading a book on wave and found that when they derive the equation of shm from the equation force varies with negetive displacement , they had taken a propotionality constant to make the force and displacement equal and they had taken frequency of the shm as the constant . So my question...

Homework Statement Find the energy eigenvalue. Homework Equations H = (p^2)/2m + 1/2m(w^2)(x^2) + λ(x^2) Hψ=Eψ The Attempt at a Solution So this is what I got so far: ((-h/2m)(∂^2/∂x^2)+(m(w^2)/2 - λ)(x^2))ψ=Eψ I'm not sure if I should solve this using a differential...

The function for simple harmonic oscillation is: Acos(ωT)+\phi Why is there an angle phi added to the function acos(ωT)?

Homework Statement (See attachment) Homework Equations x = \sqrt{\frac{\hbar}{2m \omega}} ( a + a^{\dagger} ) x = i \sqrt{\frac{\hbar m \omega}{2}} ( a^{\dagger} - a ) The Attempt at a Solution In part a) I was able to construct a separable Hamiltonian for the harmonic...

Homework Statement Consider an underdamped harmonic oscillator (Q > 1/2) with a sinusoidal driving force Focos(ωdt). (a) (5 pts) By using differential calculus find ωd that maximizes the displacement amplitude. (b) (7 pts) By using differential calculus find ωd that maximizes the velocity...

Consider a light flexible rod placed on a horizontle table with part of the rod (length say "x") hanging freely (ie without support of the table) see attachment for clarity A mass is also hung from the rod t one end. Are there any equations that relate the Period T of the end of the rod to...

Homework Statement Two springs each have spring constant k and equilibrium length (L). They are both stretched a distance (L) and attached to a mass m and two walls. At a given instant, the right spring constant is somehow magically changed to 3k (the relaxed length remains L). what is the...

Ground State Wave Equation: ψ0=(a/∏)(1/4)e(-ax2/2) Prove the Heisenberg Uncertainty principle ≥h(bar)/2 by way of expectation values. First I found <x>=0 because it was an odd function then I found <Px>=0 because it was an odd function Then <x2>=∫(a/∏)(1/2)x2e(-ax2)/2dx=1/2a by way of...

So my friend and I were going through problems and this came up... Consider 3 straight, infinitely long, equally spaced wires (with zero radius, separated each by a distance d), each carrying a current I in the same direction. blah blah blah... part c) asks us... If the middle...

I believe this is pretty standard. Given a mass m on a spring with spring constant k, a solution to the second order differential equation of motion m\ddot{x} = -kx, is x = cos ωot, and ωo = \sqrt{k/m}. If that same oscillator is driven with a force F(t) = Fo cos ωt the equation of motion...

Homework Statement A simple harmonic oscillator has an amplitude of 0.1 m. At what displacement will its kinetic and potential energies be equal? Homework Equations The Attempt at a Solution I'm trying to figure out how to solve this problem but I'm totally stuck and even don't...

I know that simple harmonic motion is a type of periodic motion where the restorative force is directly proportional to the displacement so that the time evolution is sinusoidal but is there such a thing as just harmonic motion? 0r is harmonic motion just short for simple harmonic motion?

Homework Statement The problem wants me to calculate (Δx)^2 and (Δp)^2 to find the uncertainty principle. Delta x is the variance and the problem gives the formula as.. Δx= <n|x^{2}|n>-<n|x|n>^{2}Homework Equations x=\sqrt{\frac{\hbar}{2m \omega}}(A^{-}+A^{+}) Where A+ and A- are the raising...

This is a problem I've been trying to solve for quite some time now. Any help would be appreciated. Homework Statement When a person with the mass of 105kg sits in a car, the body of the car descends by 2,5cm in total. In the car there are four shock absorbers filled with oil and a spring...

Homework Statement A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest: a.) find the force between the bottom of the box and the block as a function of time...

Homework Statement Show ln(az) where a is a real number and z = x + iy is harmonic everywhere except z = 0. Homework Equations z = x + iy = rcos(θ) + irsin(θ) = re^iθ z = u(x,y) + iv(x,y) Cauchy Riemann test for analyticity: ∂u/∂x = ∂v/∂y ∂u/∂y = -∂v/∂x The Attempt at a...

Homework Statement The displacement amplitude of a lightly damped oscillator with m=0.250kg and k=6400N/m is observed to decrease by 15% in exactly five minutes a) Calculate the fraction (in%0 of the initial mechanical energy of the oscillator that has been converted to other forms of energy...

Homework Statement A block rides on a piston that is moving vertically with simple harmonic motion. (a) If the SHM has period 2.65 s, at what amplitude of motion will the block and piston separate? Homework Equations x(t)=xmcos(ωt + ∅) a(t)=-w2xmcos(ωt + ∅) Where xm is the amplitude...

A bucket of mass 2.0 kg containing 10 kg of water is hanged on a vertical ideal spring with constant 125 N/m, oscillating up and down with an amplitude equal to 3.0 cm. Suddenly arises a leaky in the bottom of the bucket so that the water flows at constant rate of 2.0 grams/s. When the bucket...

Homework Statement A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest: a.) find the force between the bottom of the box and the block as a function of time...

Homework Statement Derive the expression v = lnfn where ln is the shortest distance between nodes for the nth harmonic. Homework Equations v = wave speed ln = shortest distance between nodes for the nthharmonic fn = frequency of the nth harmonic The Attempt at a Solution Is it...

Homework Statement Two blocks mass m1 and m2 (m1 greater than m2) are joined by a spring (which can extend and compress) and both rest on a horizontal frictionless table. the blocks are pulled apart, held at rest and then released. describe and explain as fully as you can the sibsequent...

Hello, I am trying to derive the harmonic content of a signal passing through a transistor's transfer function. After a Taylor expansion in Mathematica 7, I have the expanded equation and the next step is to reduce everything to first order Sine/Cosine functions. In Mathematica, if I have a...

Homework Statement A harmonic oscillator has angular frequency ω and amplitude A. What is the magnitude of the displacement when the elastic potential energy is equal to the kinetic energy? (Assume that U = 0 at equilibrium.) Express your answer in terms of the variables ω and A...

×Homework Statement A lift cable has mass per unit length 4kg/m. The lift has mass of 920kg (assume that the tension in the cable is provided solely by the weight it supports). When the lift stops at the 3rd floor, the distance from the top of the lift to the top of the cable is 4.6m. Assuming...

Homework Statement A block with mass m =7.1 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.5 m/s. The block oscillates on the spring without...

Homework Statement A metal sphere of mass 0.20kg is hung from a helical spring whose top end is clamped. the sphere is displaced by 0.030m below its equilibrium position, and then released. 20 cycles of oscillation, of amplitude 0.030m, occur in a time of 12.0s. calculate; (I) the spring...

Challenge Problem: A variable line $L$ passing through the point $B(2,5)$ intersects the lines $2x^2-5xy+2y^2=0$ at $P$ and $Q$. Find the locus of the point $R$ on $L$ such that distances $BP$, $BR$ and $BQ$ are in harmonic progression.

I have to solve the following D.E. which describes how the amplitude of oscillation r, changes with time. r=f(t) \frac{dr^{2}cos^{2}t}{dt}=rsint How do I find r?

hello, new here and confused about Newton second Law. given: vertical mass damper system, position of the mass: x(t)=sin(t) velocity is: v(t)=cos(t) acceleration is: a(t)=-sin(t) function x(t): above x-axis describes position of the mass below the vertical equilibrium point, which (below) is...

I need to find the value σ for which: ψ0(x) = (2πσ)-1/4 exp(-x2/4σ) is a solution for the Schrodinger equation I know the equation for the QHO is: Eψ = (P2/2m)ψ + 1/2*mw2x2ψ I've tried normalizing the wavefunction but I end up with a σ/σ term :( Any help would be greatly...

The question is: A 56.0 kg bungy-jumper hangs suspended from her bungy-cord, at rest. She is displaced from this position by 15.0 m downward, and then released. She bounces up and down, with a period of 5.800 s. Assume the woman undergoes simple harmonic motion, described by y(t) = X cos(2...

Homework Statement The motion of a particle is given by: x = (6.0m) cos(0.586t + 0.72) a) Find the amplitude b) Find the Period c) Find the first time for t>0 when v=0 d) Find the maximum acceleration e) Fine the phase at time t=1.38s Homework Equations x = A cos ωt T =...

Homework Statement A particle moving in simple harmonic motion with a period T = 1.5 s passes through the equilibrium point at time t0 = 0 with a velocity of 1.00 m/s to the right. A time t later, the particle is observed to move to the left with a velocity of 0.50 m/s. (Note the change in...

Homework Statement A spring is hung vertically from a support. A mass of 4.5 kg is hung from the lower end of the spring and is slowly lowered a distance of 22.0 cm until equilibrium is reached. This mass is then lowered to a point 15.0 cm below the equilibrium point and is then released...

Homework Statement A 250 gram mass is connected to a spring and executes simple harmonic motion. The period of motion is 0.5 seconds and the total mechanical energy is 0.50J. What is the amplitude of motion? Homework Equations ΔU = 1/2kx2 The Attempt at a Solution I get 1/2kx2 =...

Hi Here is my code to get the sum of harmonic series. Harmonic series is \sum_{i=1}^{\infty}\; \frac{1}{i} here is the code program harmonic implicit none integer :: i,n real :: sum=0.0 write(*,*)'How many terms you want to sum ?' read(*,*) n do i= 1 ,n...

I've been set this question by my tutor and I'm having difficulty doing it. A mass of 2 kg is hung from the lower end of a vertical spring and extends it by 40 cm. The mass is now pulled down a further 20 cm and is then released from rest so that it oscillates about the equilibrium position...

Over which interval do the wave functions of a harmonic oscillator form a complete and orthogonal system? Is it (-inf,+inf)? The case with particle in a box is rather clear(system is complete and orthogonal only for the interval of the well), however the harmonic oscillator is a bit less intuitive.

Hello. I was trying to find out the propagator for the inverted SHO (something like tachyon oscilltor) and turns out that it remains unitary only for very short times. Which didnt make much sense to me. I tried looking at the usual SHO propagator, and that too seems to be not Unitary! ( I...

here is a link to the pdf file with my question and answershttp://dl.dropbox.com/u/2399196/harmonic%20osc.pdf i'm not sure where to start, because i don't want to assume anything that i haven't been given. i'm stuck on part (iv) where i have to derive explicit expressions for 2 wave functions...

I've heard before that it's because when you expand around a minimum point in the potential energy you get a quadratic function, but I can't recall where I read this. Can anyone point me in the right direction, or give their own explanation? I only ask because I just solved a problem in my...