Harmonic Definition and 1000 Threads

Homework Statement Which of these forces could result in simple harmonic motion F(x)=−9(x−7)3 F(x)=−9x+7 F(x)=−9x3 F(x)=−9x F(x)=9x F(x)=9x3 9x3 is 9x^3, same with itsopposite Homework Equations F=kx, the definition of shm The Attempt at a Solution I figured -9x and 9x were the only...

Homework Statement [/B] The isotropic harmonic oscillator in 2 dimensions is described by the Hamiltonian $$\hat H_0 = \sum_i \left\{\frac{\hat{p_i}^2}{ 2m} + \frac{1}{2} m\omega^2 \hat{q_i}^2 \right\} ,$$ for ##i = 1, 2 ## and has energy eigenvalues ##E_n = (n + 1)\hbar \omega \equiv (n_1 +...

Homework Statement Prove that: x=8sin2t+6cos2t is undergoing S.H.M. (Not too sure about how to prove for solution.) Homework Equations Solution for S.H.M. x=asin(nt+α) is \frac{d^{2}x}{dy^{2}}=-n^2xThe Attempt at a Solution...

Homework Statement A mass on a spring has an angular oscillation frequency of 2.56 rad/s. The spring constant is 27.2 N/m, and the system's kinetic energy is 4.16 J when t = 1.56 s. What is the oscillation amplitude? Assume that the mass is at its equilibrium position when t = 0.a. 63.1 cm b...

Homework Statement The velocity of a particle is related to its position by: v2 = w2 (A2 - x2) where w and A are constants. Show that the acceleration is given by: a=-w2x[/B]Homework EquationsThe Attempt at a Solution a= v* dv/dt v=(A2w2-x2w2)1/2 dv/dt= 1/2 (A2w2-x2w2)-1/2 * -2xw2 v *...

Homework Statement What length must the pendulum be changed to in order to show the correct time? L=0.5m After 12hours the clock is behind by 30minutes. Homework Equations w=sqrt(g/L) w=2πf The Attempt at a Solution I thought if I set the frequency equal to 1Hz and solved for length it would...

Hello! An assignment for my computational modeling course is to demonstrate the use of the Standard Euler method for modeling a simple harmonic oscillator; in this case, a mass attached to the end of a spring. I have the two coupled first-order differential equations satisfying hookes law...

Homework Statement [/B] Consider a gas of N weakly interacting bosons trapped in a 3d harmonic potential ##V = \frac{1}{2}mw^2 (x^2 + y^2 + z^2)##. The single particle quantum states have energies ##\epsilon = \hbar w (n_x + n_y + n_z + 3/2)##. Calculate the total number of quantum states...

Homework Statement I must find the average number of energy levels of quantum harmonic oscillator at temperature T, and the answer is given as I must use Boltzmann distribution and the sum of geometric progression. For finding the average value I must use the equation <F>=trace(F*rho)...

Homework Statement A mass m = 750 g is connected to a spring with spring constant k = 1.5 N/m. At t = 0 the mass is set into simple harmonic motion (no damping) with the initial conditions represented by the point P in the phase space diagram at the right. **(This phase space diagram has...

Homework Statement A harmonic potential is parameterised as: V(x)=\frac{k}{2}(x-x_{0})^2An object moves within this potential with a total energy E > 0. (i) Where are the two turning points of the motion xA and xB? (ii) Write down the equation of motion for the object, and use it to find...

Homework Statement A mass m sits on a horizontal frictionless surface and is attached to a wall by means of a spring having force constant k. The mass is now subjected to an additional force of the form. F(t) = Acosbt (a) Write the equation of motion for this mass.(b) What is the solution to...

Homework Statement http://i.imgur.com/u8vUv5a.jpg Find the phase constant. Homework Equations x(t)=Acos(ωt + Φ) v(t)=-Aωsin(ωt + Φ) Vmax = ωA ω=2π/T The Attempt at a Solution ω = 2π/12 = 0.5236 A = 60/0.5236 = 114.59 cm v(0) = -30 = -114.59(0.5236)sinΦ 0.5 = sinΦ Φ = π/6 and 5π/6. Which...

Homework Statement The position of a 50 g oscillating mass is given by x(t)=(2.0cm)cos(10t−π/4), where t is in s. If necessary, round your answers to three significant figures. Determine: The total energy. Homework Equations T = 2π/w T = 2π√m/k 1/2kA^2 1/2mv^2 1/2kx^2 The Attempt at a Solution...

Relaxation time is defined as the time taken for mechanical energy to decay to 1/e of its original value. Why do we take a specific ratio of 1/e? What is its significance?

1. After finding out that the wave function ##\Psi(z) \sim Ae^{\frac{-z^{2}}{2}}## in the limit of plus or minus infinity Griffiths separates the function into two parts ##\Psi(z)=h(z)e^{\frac{-z^{2}}{2}}## My question will be about a certain aspect of the function ##h(z)## After solving the...

Homework Statement I have a question about simple harmonic motion: Where it says " if we denote the ratio k/m with the symbol omega squared ... ": I know it says that they chose omega squared to make the solution simpler, but I mean, to me it doesn't really make sense. Omega is associated...

My question is how we describe a harmonic oscillate. Wikipedia says, "a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x." My question is, how is the harmonic oscillator a "system"? I thought...

I'm a bit confused wether or not there is a link between harmonic functions (solutions of the Laplace pde) and harmonic oscillating systems? What is the meaning of "harmonic" in these cases? Thanks!

My problem is described in the animation that I posted on Youtube: For the sake of convenience I am copying here the text that follows the animation: I have made this animation in order to present my little puzzle with the quantum harmonic oscillator. Think about a classical oscillator, a...

Consider a vertical pendulum affected by gravity (See the pdf file i included). Now i can choose two different opposite directions for my unit vectors which give me different equations. \downarrow : m\ddot x = mg-kx \uparrow : m\ddot x = kx-mg Which of course makes perfect sense, changing...

Homework Statement An oscillator with mass 0.5 kg, stiffness 100 N/m, and mechanical resistance 1.4 kg/s is driven by a sinusoidal force of amplitude 2 N. Plot the speed amplitude and the phase angle between the displacement and speed as a function of the driving frequency and find the...

Homework Statement A mass m is sliding back and forth in a simple harmonic motion (SHM) with an amplitude A on a horizontal frictionless surface. At a point a distance L away from equilibrium, the speed of the plate is vL (vL is larger than zero). Homework Equations What is the period of the...

Hi pf. I have a question about an experiment. If you lie a ruler horizontally across two supports (one near each end) and then hang a weight in the middle it will undergo SHM if you pull the mass down. If you move the supports in closer it will oscillate with a higher frequency. I just wanted to...

Homework Statement three harmonic function of frequency p, 2p ,3p were added together. what is the frequency of resultant periodic function? Homework Equations X=Asin(wt) A-amplitude w-frequency X=X1+X2+X3 The Attempt at a Solution need a hint ..

Hi there, I am reading an introduction on trapping atoms in space with magnetic potential. The article said the lab usually use a harmonic potential to trap the atoms and the potentials is in the form ##\dfrac{m}{2}(\omega_x^2x^2 + \omega_y^2y^2 + \omega_z^2z^2)## and ##\omega_{x,y,z}## has...

Homework Statement Before I write the question you should know that my maths is all correct in my solution but I must have used the formulas incorrectly (or used the wrong formulas). I can't pinpoint where I've gone wrong or if I have left a formula out (I'm a teacher solving this question for...

Homework Statement So I have to write a report based on an experiment that I have conducted. I know that my report is connected with Simple Harmonic motion and Elastic force, but I do not know how to describe it in a more efficient/scientific way. Essentially, I am dropping a weight (constant)...

Homework Statement The ground state of the wavefunction for an electron in a simple one-dimensional harmonic potential well is \Psi _{0}(x)= \left ( \frac{m\omega }{\pi \hbar} \right )^{1/4} exp(-\frac{m\omega x^{2}}{2\hbar}) By employing first-order perturbation theory calculate the energy...

Prove the following $$\sum_{k=1}^n \frac{H_k}{k} = \frac{H_n^2+H^{(2)}_n}{2}$$ where we define $$H^{(k)}_n = \sum_{j=1}^n \frac{1}{j^k} \,\,\, ; \,\,\, H^2_n = \left( \sum_{j=1}^n \frac{1}{j}\right)^2 $$

*note: my previous thread will be deleted because I didn't include relevant equations + I put two unrelated problems in the same thread. 1. Homework Statement A cat bobble head doll consists of a weighted head on top of a spring. When the head hangs straight sown in equilibrium, it is observed...

Homework Statement [/B] A mass-spring system is oscillating with an amplitude of 10.0 cm. What is the speed of the mass at a location where the kinetic energy of the mass and the potential energy of the spring are equal? I want to know if it's possible to solve for just a number, that is, not...

Homework Statement Given the coherent state of the harmonic oscillator |z>=e^{-\frac{|z|^2}{2}}\sum_{n=0}^\infty\frac{z^{n}}{\sqrt{n!}}|n> compute the probability for finding n quanta in the sate |z> and the average excitation number <z|n|z>Homework Equations...

I did an experiment at school, and the experiment SET UP that i did is basically shown in the word attachment link. http://www.schoolphysics.co.uk/age16-19/Mechanics/Statics/experiments/bending_of_a_beam.doc. I have two questions! Question 1:when i did the experiment, I found that with a...

Homework Statement proxy.php The graph shows a snapshot of a traveling harmonic wave; eight points are indicated. Answer the five questions by selecting from the choices below. A) → B) ← C) ↓ D) ↑ E) the velocity is zero If the wave is moving to the right, what is the direction of the...

If $$f(z)=u(x,y)+iv(x,y)$$ is analytic in a domain D, then both u and v satisfy Laplace's equations $$\nabla^2 u=u_{xx} + u_{yy}=0$$ $$\nabla^2 v=v_{xx} + v_{yy}=0$$ and u and v are called harmonic functions. My question is whether or not this goes both ways. If you have two functions u...

explain this derivation: Source: microwave engineering, pozar Why did pozar use those conjugates? What does the source current mean?

Hi, For a wave fixed at both ends, what is the behaviour of the original and refelcted wave between the harmonic frequencies? I understand how a standing wave is created by the superposition of a wave and it;s reflection at a boundary. I also understand that at the fundamental frequency of the...

for harmonic oscillator, V(x) = 1/2*m*w^2*x^2. here, the spring can be stretch or compress. however, is if the spring can only stretch such that V(x) is infinity for x<0, then find energy level for this setup. I don't understand the part about spring only being able to stretch. what does that...

Homework Statement There is a harmonic oscillator with charge q and sudenly we turn on external electric field E, which direction is the same as oscillator's. We need to find probability, that particles energy calculated in electric field will be in m state. n=1, m=2 2. Homework Equations The...

I know this is simple, but I don't fully understand why the motion of a piston is considered to be simple harmonic? Wouldn't the piston and connecting rod have mass?

Homework Statement A horizontal plank of mass m and length L is pivoted at one end. The plank's other end is supported by a spring of force constant k (see the figure below). The plank is displaced by a small angle θ from its horizontal equilibrium position and released. Find the angular...

Homework Statement One end of a light hacksaw blade is clamped in a vise with the long axis of the blade horizontal and with the sides vertical. A 0.665- kg mass is attached to the free end. When a steady sideways force of 20.5 N is applied to the mass it moves aside 13.3 cm from its...

Given a position vs time graph of simple harmonic motion of an object and using the equation x(t) = xo = A sin (ωt +Φ), how am I supposed to find Φ? I can easily find A and the period (T). I also know T = 2 pi / ω, so I can find ω. But I don't know x(t) and t. I tried finding random points in...

For one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, could be obtained by means of Newton's second law and Hooke's law and i don't get this part which...

Homework Statement Homework Equations acceleration = -(2*pi*f)^2 * x, where f is the frequency and x is the displacement from equilibrium. The Attempt at a Solution I thought the acceleration would be greatest when the displacement from equilibrium is greatest, so at point P, but the answer...

Homework Statement http://puu.sh/cAjmp/14ba3df23a.jpg Homework Equations Acceleration at any instant: -(2*pi*f)^2 * x, where x is displacement from equilibrium and f is frequency. The Attempt at a Solution Firstly, I know it can't be D as acceleration would increase as potential energy...

Homework Statement [/B] Write the second-order equation for the harmonic oscillator, y ̈ + ω2y = 0 as two linear ordinary differential equations. What is the analytic solution y(t) if ω = 2π, y(0) = 1 and y′(0) = 0? Homework EquationsThe Attempt at a Solution So, I have to write some...

Homework Statement Actually this is not a problem. This is about something i couldn't understand. Homework Equations where wt equals θ The Attempt at a Solution I can understand that x=r.cosθ it is obvious. But i can't understand why Vx=-V.sin(w.t) When i take a triangle from that...

Homework Statement The problem requires to solve the integration to find ## G(t) ## after ##G(\omega)## is found via Fourier transform. We have G(\omega)= \frac{1}{2\pi}\frac{1}{\omega _{0}^2 - \omega ^2} Homework Equations As mentioned previously, the question asks to find ##G(t)## The...