Harmonic Definition and 1000 Threads

In Simple Harmonic Motion, can (k/m) = ω2 be expressed for all SHMs or only the ones in which the mass due to which the SHM is being executed is performing a circular motion? Since for example, in the case of spring, there is no circular motion involved, so omega should not be defined for...

Homework Statement When completing this problem I am able to find a value for the phase angle but am unsure of how to find the quadrant for the phase angle therefore unable to get the correct phase angle. Homework Equations Provided in the question: x = xmcos(wt+ phi) The Attempt at a...

Homework Statement I seem to have problems finding time in SHM. To find the time after projection, I know that either x=asinωt or x=acosωt needs to be used, so since R is projected away from O, it means that it is moving towards the equilibrium position, therefore I used x=acosωt to find the...

I'm not really sure by the definition given by my textbook. Is it basically the breakdown of a sound wave into its fundamental frequency and other harmonics?

Homework Statement Two springs each have spring constant k and equilibrium length ℓ. They are both stretched a distance ℓ and then attached to a mass m and two walls (which are 4 ℓ apart). At a given instant, the right spring constant is somehow magically changed to 3k (the relaxed length...

Homework Statement Consider a linear harmonic oscillator with the solution defined by the ladder operators a and a†. Use the number basis |n⟩ to do the following. a) Construct a linear combination of |0⟩ and |1⟩ to form a state |ψ⟩ such that ⟨ψ|X|ψ⟩ is as large as possible. b) Suppose that...

Homework Statement At time t = 0, a point starts oscillating on the x - axis according to the law x = a sin(ωt). Find the average velocity vector projection (I assume it means magnitude based on previous questions in the book). Homework Equations The Attempt at a Solution I knew that the...

Hi i want to find propagator of inverse harmonic oscillator to find time dependent wave function, but I can't have any ideas about this. Is it possible to help me to find it Thanks

hy physics forum, I am doing an advanced qm course, but i still have some doubts about the correct formalism and so on.. so i have this problem of a one-dimensional harm. oscillator including 2 bosons. the hamiltonian would thus be ## \hat{H}=1/2 (\hat{p_1}^2+\hat{p_2}^2+\omega...

Homework Statement A linear harmonic oscillator with frequency ω = hbar / M is at time t = 0 in the state described by the wave-function: Ψ(x,0) = C( 1 + √2x) e-x2/2 Determine the values of energy which can be measured in this state. I'm not really sure where to start this question and was...

I'm a bit unsure about my answers. Help! (posting figure) link: http://imgur.com/whExO3S Homework Statement http://imgur.com/whExO3S Consider the harmonic oscillator composed of a mass and two springs of spring constants k1 and k2 (shown in figure). If the mass, M moves on a friction less...

I studied this from Griffith Chapter 2, with the algebraic (raising and lowering operator) method, we reached the ground state by setting a_Ψ0 = 0 , then we got what the ground state is, and then plugged it in the Schrodinger equation to know the energy, and it turned out to be 0.5 ħω. My...

Homework Statement Consider the one-dimensional harmonic oscillator of frequency ω0: H0 = 1/2m p2 + m/2 ω02 x2 Let the oscillator be in its ground state at t = 0, and be subject to the perturbation Vˆ = 1/2 mω2xˆ2 cos( ωt )at t > 0. (a) Identify the single excited eigenstate of H0 for...

(2.) Let the differential equation ¨x + 2 ˙x + 2x = 6 sin(t)U(t − 3π/2) , x(0) = 2, x˙(0) = 2 Solve for the position function x(t) using the Laplace transform:

(a) A wave traveling on a Slinky® that is stretched to 4.5 m takes 2.6 s to travel the length of the Slinky and back again. What is the speed of the wave? For this one, I did v = d/t = 4.5 m / 2.6 s = 1.73 m/s Then I did v = (1.73)(2) = 3.46 m/s This is correct (b) Using the same Slinky...

Homework Statement A 15.0-N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as a function of time t is given by y(t)=4.50 cos[(19.5s−1)t−π/8] in centimeters. What is the spring constant of the spring? Homework Equations y...

Homework Statement Show that for the one-dimensional linear harmonic oscillator the Hamiltonian is: [; H = \frac{1}{2}[P^2+\omega ^2 X^2]-\frac{1}{2}\omega \hbar ;] [; =\frac{1}{2}[P+i\omega X][P-i\omega X]+\frac{1}{2} \omega \hbar ;] where P, X are the momentum and position operators...

I have read a book that demonstrate the origin of electrical susceptibility of high order in harmonic generation: (in Robert Boyd's book : "Nonlinear optics"). For example, he show clearly for the case of second harmonic generation, how \chi^{(2)} depends on matrix element of electric dipole...

Homework Statement Two positive charges +Q are held fixed a distance apart. A particle of negative charge -q and mass m is placed midway between them, then is given a small displacement x perpendicular to the line joining them and released. Show that the particle describes simple harmonic...

Homework Statement A 4.0kg block is suspended from a spring with force constant of 500N/m. A 50g bullet is fired into the block from directly below with a speed of 150m/s and is imbedded in the block. Find the amplitude of the resulting simple harmonic motion. Homework Equations F=-kx...

Homework Statement A 775 g mass is hung on a spring. As a result the spring stretches 20.5 cm. If the object is then pulled an additional 3.0 cm downward and released, what is the period of the resulting oscillation? Homework Equations T = 2pi sqr root(m/k) Hooke's Law Fs=kx The Attempt at a...

Homework Statement To work out the intial acceleration, do we just use the equation: So at t = 0 We eliminate the wt inside the bracket, and are left with Aω^(2)sin(Φ + π) Homework EquationsThe Attempt at a Solution The part which I'm not so sure on, is if i have values for Φ, do i...

Homework Statement An object of mass 0.2kg is hung from a spring whose spring constant is 80N/m. The object is subject to a resistive force given by -bv, where v is it's velocity in meters per second. If the damped frequency is √(3)/2 of the undamped frequency, what is the value of b...

Homework Statement A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is oscillating on a frictionless, horizontal surface with an amplitude of 2.00 m. A 6.00-kg object is dropped vertically on top of the 4.00-kg object as it passes through its equilibrium...

Homework Statement "Which of the following applications would have the most benefit from a short damping time?" a. bathroom scale b. child jolly jumper c. suspension on passenger car d. suspension on race car Homework EquationsThe Attempt at a Solution Im assuming that both A and D should be...

Homework Statement At t=0 the wave function of a two-dimensional isotropic harmonic oscilator is ψ(x,y,0)=A(4α^2 x^2+2αy+4α^2 xy-2) e^((-α^2 x^2)/2) e^((-α^2 y^2)/2) where A its the normalization constant In which instant. Wich values of total energy can we find and which probability...

Homework Statement For a quantum harmonic oscillator in an electric field, using ##\hat{V}=q\epsilon\hat{x}##, with the following trial state: $$|\psi\rangle=|0\rangle+b|1\rangle$$ Show that the energy can be written as $$E=\frac{\frac{\hbar...

Homework Statement A woman bungee-jumper of mass 50 kg is attached to an elastic rope of natural length 15 m. The rope behaves like a spring of spring constant k = 220 N/m. The other end of the spring is attached to a high bridge. The woman jumps from the bridge. a) Determine how far below...

Homework Statement Is the statement cirrect: "the rate at which a wave transfers energy depends on the amplitude at which the particles of the medium are vibrating." And does the energy=A^2 ? Homework Equations E (proportional) A^2 The Attempt at a Solution For the statement I am about...

I translated it, so the notation may not be so great. You have a vertical spring with a spring constant of 16 N.m^-1, we attach to its lower end a body with a mass of 0,4 KG and form a system which oscillates on a straight line with length of 8cm, we assume that at the start of the time, the...

Homework Statement The Hamiltonian is given by: H = \frac{1}{2} \sum_{i=1,2}[p_i^2 + q_i^2] We define the following operators: J = \frac{1}{2} (a_1^+ a_1 + a_2^+ a_2) J_1 = \frac{1}{2} (a_2^+ a_1 + a_1^+ a_2) J = \frac{i}{2} (a_2^+ a_1 - a_1^+ a_2) J = \frac{1}{2} (a_1^+ a_1 - a_2^+...

The ground state wave-function of a 1-D harmonic oscillator is $$ \psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}). $$ a) find Average potential energy ? $$ \overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2} $$ b) find Average kinetic energy ? $$ \overline{T} =...

Homework Statement A 4.00kg block is suspended from a spring with k = 500N/m. A 50.0g bullet is fired into the block from directly below with a speed of 125m/s and becomes embedded in the block. a) Find the amplitude of the resulting SHM. b) What percentage of the original kinetic energy of...

Homework Statement A particle in SHM is subject to a driving force F(t)= ma*e^(-jt). Initial position and speed equal 0. Find x(t). Homework Equations F = -kxdx = mvdv F(t) = F(0)*e^(iωt) x(t) = Acos (ωt +φ) The Attempt at a Solution I have no idea how to deal with the exponential term. I...

Homework Statement A metal wire is vibrating at its third-harmonic frequency. 0.32 m from one end, the amplitude is equal to one quarter the maximum amplitude. Find the length of the wire. Homework EquationsThe Attempt at a Solution I don't quite understand the question, it says 0.32m from one...

Homework Statement The problem asked me to derive an expression for the stationary wave function of the 3d harmonic oscillator which I have done. It then tells me a particle is in the stationary state $$\psi_{n_x,n_y,n_z}(x,y,z)=\psi_{100}(x,y,z)$$ and to express this in spherical coordinates...

Homework Statement An incident wave frequency f =500Hz , power Wi = 50 W and amplitude Ai= 5 mm spreads to the positive x in a linear density rope u1 unknown. When the wave encounters another rope ( attached to the first at a point P) density linear u2= 64 g/m (such as u2>u1 ) , The...

I was wondering how to derive the sinusoidal equation for the simple armonic oscillator. But I am currently trying to understand this step in this webpage: I don't get where do P and Q come from and why it is summing pe^iwt + qe^-iwt. please I need some help. The rest of it pretty much makes...

Hey, this is more of a "share" theard, instead of a "Question" thread. I am starting my second year in a Phisics BS.c. I noticed that while poeple around me at school centinly understand HO's as well as I do, I seem to be one of the only ones who is really enjoying the subject. It is my...

Hi everyone, first time post here. I know (or at least think I know) that strings can sympathetically resonate at harmonic intervals. For example, a string whose fundamental is 400Hz is able to resonate at 800Hz if it's excited by a 800Hz source. Maybe I'm wrong on that as well? heh.. Anyways...

Hi everyone I was wondering, why is vacuum energy related to the zero point energy of an harmonic oscillator? The hamiltonian of an harmonic oscillator is $H= \frac{p^{2}}{2m} + \frac{1}{2} \omega x^{2}$. Where does the harmonic potential term come from in the vacuum?

A voltage amplifier ideally should have the input-output relationship of vo = 100vi but in practice the relationship is vo = vi(98 + 2vi). Calculate the %age second harmonic distortion present in the amplifier’s output for a sinusoidal input of 10 mV r.m.s % harmonic distortion = amplitude of...

Homework Statement No friction. m3=5m, m2=12m, m1=3m Prove that the system's acceleration when it's released is a=0.2g. is it the max acceleration? Show that the equilibrium point is at x0=0.75L Show that the kinetic energy of the system is E=mgL Show that m2 will stop momentarily at...

Homework Statement We have the lagragian L = \frac{m}{2} \dot{x}^2 - \frac{m \omega x^2}{2} + f(t) x(t) where f(t) = f_0 for 0 \le t \le T 0 otherwise. The only diagram that survives in the s -matrix expansion when calculating <0|S|0> is D = \int dt dt' f(t)f(t') <0|T x(t)x(t')|0>...

I was thinking about harmonic oscillators last night when explaining the non-zero ground state energy of the quantum version to a non-scientific friend and the conversation pushed my curiosity a little so I'm wondering if anyone happens to know about any books solely about harmonic oscillators...

So, I am following the PI lecture series by Neil Turok. He starts with the following description of harmonic gauge condition $$g^{\mu \nu}\Gamma^{\lambda}_{\mu \nu}=0$$ He then claims that for linearized gravity (weak field) i.e. $$g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} $$ with $$ |h_{\mu...

Homework Statement Derive the natural frequency f_n of the system composed of two homogeneous circular cylinders, each of mass M, and the connecting link \text{AB} of mass m. Assume small oscillations. Homework Equations The sum of the kinetic + potential energies in an isolated system...

Hi, I am trying to find the wavefunction of a coherent state of the harmonic oscillator ( potential mw2x2/2 ) with eigenvalue of the lowering operator: b. I know you can do this is many ways, but I cannot figure out why this particular method does not work. It can be shown (and you can find...

Homework Statement A simple harmonic oscillator consists of a block of mass 45 g attached to a spring of spring constant 240 N/m, oscillating on a frictionless surface. If the block is displaced 3.5 cm from its equilibrium position and released with an initial velocity of 2.5 m/s, what is its...

A simple harmonic oscillator consists of a block of mass 45 g attached to a spring of spring constant 240 N/m, oscillating on a frictionless surface. If the block is displaced 3.5 cm from its equilibrium position and released so that its initial velocity is zero, what is the phase constant, φ ...