Harmonic Definition and 1000 Threads

Im kind of confused on which acceleration equation to use. A = -(kx)/m or A = -(w^2)Acos[(angular freq)(time) + phase constant] as both of these contribute to SHM. Im guessing I can use the first acceleration equation when i know how far the object stretched and if i don't i...

Homework Statement Homework Equations The Attempt at a Solution

Okay, so if a harmonic oscillator has a restoring force given by Hooke's Law such that Fs = -kx and its integral gives the potential energy associated with the restoring force: PE = -(1/2)kx2 Then for the total energy of a harmonic oscillator, why is the TE: TE = Evibration +...

Homework Statement A mass m hanging on a spring oscillates vertically. If the equilibrium point of the oscillation is a distance d below the relaxed length of the spring and if the amplitude of the oscillation is A, what is the maximum kinetic energy of the oscillation?[b]2. Homework Equations...

I have done a handful of problems related to sound waves in air columns and one thing I have noticed is that, unless told otherwise in the problem formulation, one always assumes that sound wave that is formed is always the fundamental harmonic and thus the length of the air column comprises a...

Why do all wine glass have four nodes (4th harmonic)?? Why do wine glass have four nodes... or four anitnodes... (4th harmonic)?

Homework Statement For the n = 1 harmonic oscillator wave function, find the probability p that, in an experiment which measures position, the particle will be found within a distance d = (mk)-1/4√ħ/2 of the origin. (Hint: Assume that the value of the integral α = ∫01/2 x2e-x2/2 dx is known...

Homework Statement A 24-lb weight, attached to the end of a spring, stretches it 4 inches. Find the equation of motion if the weight is released from rest from a point 3 inches above the equilibrium position. Homework Equations \frac{d^{2}{x}}{dt^2}+\frac{k}{m}x=0 F=ma The Attempt...

what is the limitation of T = 2π \sqrt{\frac{m}{k}}

Hi all Homework Statement I have the first three states of the harmonic oscillator, and I need to know the amplitudes for the states after the potential is dropped.Homework Equations u_{0}=(\frac{1}{\pi a^{2}})^{\frac{1}{4}} e^{{\frac{-x^2}{2a^2}}} u_{1}=(\frac{4}{\pi})^{\frac{1}{4}}...

Problem: In a harmonic oscillator \left\langle V \right\rangle=\left\langle K \right\rangle=\frac{E_{0}}{2} How does this result compare with the classical values of K and V? Solution: For a classical harmonic oscillator V=1/2kx^2 K=1/2mv^2 I don't really know where to begin. Is it safe...

Prove the following : $\displaystyle \psi(n)= -\gamma \,+\,\sum^{n-1}_{k=1}\frac{1}{k}$

Homework Statement A damped oscillator is subjected to a simple harmonic force, satisfying $$\ddot{x}(t) + 2k\dot{x}(t) + \omega^2x(t) = g \cos (nt), $$where ##g, k, \omega, n +ve.## 1) Show that for ##t >>1/k## the position x(t) has the form ##A \cos (nt - \phi)##, and find A and ##\phi##...

Homework Statement Consider a system of N distinguishable, non-interacting harmonic oscillators. The Hamiltonian is given (shown below). Assuming that the oscillators obey Schrodinger's equation, determine the canonical partition function for the system. Then assume the oscillators obey...

Hello! I have this general question regarding (musical) frequencies: I'm having a bit of a hard time putting what makes logical sense to me, as opposed to what I'm being taught in school. My teacher is basically saying the following: If the fraction/division of two frequencies is rational, the...

Homework Statement the problem and a possible solution(obtained from a book) is attached as a pdf to the post.However Iam unable to understand it.Please download the attachment. Homework Equations equation no (2) in the pdf.Is there any use of space translation operator in here.The Attempt at...

Homework Statement Not exactly sure why a time value of 0.500s is given, but I am positive it is why my answer isn't correct: Q. a 1kg object is attached to a horizontal spring. The spring is initially stretched by 0.100m and the object is released from rest there. It proceeds to move...

Homework Statement A particl of mass m in the potential V(x) (1/2)*mω^{2}x^{2} has the initial wave function ψ(x,0) = Ae^{-αε^2}. a) Find out A. b) Determine the probability that E_{0} = hω/2 turns up, when a measuremen of energy is performed. Same for E_{1} = 3hω/2 c) What energy...

Homework Statement 1)Consider a particle subject to the following force ##F = 4/x^2 - 1## for x>0. What is the particle's maximal velocity and where is it attained? 2)A particle of unit mass moves along positive x-axis under the force ##F=36/x^3 - 9/x^2## a)Given that E<0 find the turning...

Homework Statement Find a value for n for which the nth partial sum is ensured to approximate the sum of the alternating harmonic infinite series to three decimal places. Homework Equations Sn = Ʃ(-1)^k+1*1/k = 1 - 1/2 + 1/3 - 1/4 + 1/5 - . . . S1 = 1 S2 = 1 - 1/2 S3 = 1 - 1/2 + 1/3 S4...

Homework Statement We have U-shaped tube filled with liquid , if liquid is displaced through length 'x' find time period of SHM please help me :confused:

Homework Statement A massless spring hangs down from a support, with its lower end at y=0, where the y-axis is vertical and points downward (normal orientation of y). When a small unknown mass is attached to the spring, the lower end of the spring moves down to a position y_0 for the mass...

Homework Statement Write down the v=1 eigenfunction for the harmonic oscillator. Substitute this eigenfunction into the Schrodinger equation and show that the eigenvalue is (3/2)hν. Homework Equations The Attempt at a Solution I'm not really sure on how to to this, but here's...

Homework Statement I am unsure as to a step in Griffiths's derivation of the quantum harmonic oscillator. In particular, I am wondering how he arrived at the equations at the top of the second attached photo, from the last equation (at the bottom) of the first photo (which is the recursion...

Hi, Consider a block of mass M connected to a spring of mass m and stiffness k horizontally on a frictionless table. We elongate the block some distance, and then release it so that it now oscillates. According to the theoretical study using energy methods, we see that the mass of the...

Homework Statement Dear Guys, Does f(x,t)=exp[-i(ax+bt)^2] qualify as a harmonic waves? Please help! Manish Germany Homework Equations The Attempt at a Solution it is of the form g(ax+bt). which is the general form for harmonic wave. but what bothers me is the...

Dear Guys, Does f(x,t)=exp[-i(ax+bt)^2] qualify as a harmonic wave? Please help! Manish Germany

Homework Statement I have a ball of 20 kg describing a damped harmonic movement, ie, m*∂^2(x)+R*∂x+K*x=0, with m=mass, R=resistance, K=spring constant. The initial position is x(0)=1, the initial velocity is v(0)=0. Knowing that v(1)=0.5, v(2)=0.3, I have to calculate K and R...

So I am trying to model a harmonic oscillator floating on the oceans surface. I treated this as a harmonic oscillator within a harmonic oscillator and I am not sure if I am heading in the correct direction. Just to be clear this isn't a homework problem just something I am working on. The...

Homework Statement A meterstick is clamped to a tabletop. The end of the meter stick is deflected downwards a small distance x and is released such the end of the meterstick moves up and down in simple harmonic motion. The meterstick is measured to oscillate up and down 10 times in 5.0...

Homework Statement A 100g particle hangs freely at rest on the end of a spring of stiffness 10N/m. If the particle is projected upwards with a speed of 2m/s, find the time taken until it first comes to rest and the distance travelled. Homework Equations Well, there's F = -k.x and of course the...

It isn't making any intuitive sense. If it isn't moving in circular motion, how can it have angular frequency or speed? Also, v=\pm ω\sqrt { A^{ 2 }-x^{ 2 } } only applies to SHM with springs only, right? Also, does anyone know how to derive this equation below? x=\frac { \pm \sqrt { { { v...

Homework Statement Find the resultant of the superpostion of two harmonic waves in the form E=Ecos(α-ωt) with amplitudes of 3 and 4 and phases of π/6 and π/2 respectively. Both waves have a period of 1s. Homework Equations ω=2πf = 2π/t The Attempt at a Solution I first...

Hello, I want to include kinetic friction into the harmonic oscillator. A small blocks is attached to a horiontal spring on a table. Because there is kinetic friction there are two forces on the blok that we need to describe the oscillation. First, the force that the spring exerts and second...

Homework Statement Homework Equations F = -dU/dx The Attempt at a Solution U = \frac{1}{2}kx^2 + mgxsin\theta \\\\ F = -(kx + mgsin\theta) \\\\ F = -kx - mgsin\theta \\\\ We want to set the force = 0 because that's when the block is in equilibrium with no forces acting on...

Homework Statement Show that the following is an eigenfunction of \hat{H}_{QHO} and hence find the corresponding eigenvalue: u(q)=A (1-2q^2) e^\frac{-q^2} {2} Homework Equations Hamiltonian for 1D QHO of mass m \hat{H}_{QHO} = \frac{\hat{p}^2}{2m} + \frac{1}{2} m \omega^2 x^2...

This is not really a homework problem but rather a question about an equation for displacement in damped harmonic oscillations that I've come across during revision for midterms. In my notes and in various textbooks the equation is given as x=C\mathrm{exp}(-\frac{b}{2m}t)\cdot\mathrm{exp}(\pm...

Homework Statement In my notes it is stated that an integrator adds a phase lag of -Pi/2 and thus can cause instability. I want to understand what this really means and am deviating from the notes somewhat so do not know if I am barking up the wrong tree. Homework Equations Given a...

Homework Statement Particle of mass m undergoes simple harmonic motion along the x axis Normalised eigenfunctions of the particle correspond to the energy levels E_n = (n+ 1/2)\hbar\omega\ \ \ \ (n=0,1,2,3...) For the two lowest energy levels the eigenfunctions expressed in natural...

Period does not depend on amplitude. Correct? I deduced this from the equations for simple harmonic motion: ω=2πf ω=√(k/m)

Their equations are identical. Is there any difference between the two?

x(t)=Acos(ωt+ϕ)\\v(t)=-ωAsin(ωt+ϕ) I think my physics professor said in one of the lectures that: after setting up your position function by finding amplitude, angular speed, and solving for ϕ by setting t=0 and using the x(0) value given in the question, you need to to set t=0 in the velocity...

Homework Statement A mass is attached to a spring with a force constant of 32N/m. The spring and the mass are set into simple harmonic motion on a frictionless, horizontal surface. The period of vibration of this mass is 0.4 seconds. a) Calculate the object's mass b) Calculate...

Homework Statement Ok, basically I need to show that Ʃ 1/n (between 1 and n) (which is harmonic number) is θ (big theta) of ln(n), which means that is it bounded below and above by this function(upper and lower bound). But I don't quite understand how to prove it.Homework Equations I know...

Homework Statement Consider as an unperturbed system H0 a simple harmonic oscillator with mass m, spring constant k and natural frequency w = sqrt(k/m), and a perturbation H1 = k′x = k′sqrt(hbar/2m)(a+ + a−) Determine the exact ground state energy and wave function of the perturbed system...

Homework Statement Consider a system of N localized particles moving under the influence of a quantum, 1D, harmonic oscillator potential of frequency ω. The energy of the system is given by E=(1/2)N\hbarω + M\hbarω where M is the total number of quanta in the system. compute the total...

Trust me this is not homework... My last two questions were removed cause they looked like homework... I understand its the forum policy... From now on I will post the 'seemingly homework' on the homework sections... Suppose,there's a rod of mass m1 hanging from a point... And a mass m2 is...

Hey, My question is on determing the expectation value of position of the Harmonic Oscillator using raising and lowering operators, the question is part d) below: I have determined the position operator to be: \hat{x}=\sqrt{\frac{\hbar}{2m\omega}}(a+a^{\dagger}) and so the...

Homework Statement Prove that that the power given by \bar{P} = \frac{1}{2} \gamma m \omega_r^2 A_{(\omega)}^2 is at a maximum for \omega_r = \omega_0 Only variable is \omega_r \omega_r is the resonant frequency of the external force while \omega_0 is the eigen frequency of the...

Homework Statement The position of a mass that is oscillating on a Slinky (which acts as a simple harmonic oscillator) is given by 18.5 cm cos[ 18.0 s-1t]. What is the speed of the mass when t = 0.360 s? Homework Equations x(t)=Acos(ωt+θ) v(t)=-Aωsin(ωt+θ) The Attempt at a Solution...