Harmonic Definition and 1000 Threads

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...

Homework Statement In a port the tide and the low tide change with harmonic motion. at the high tide the water level is 12 meters and at the low tide it is 2 meters. between the tide and the low tide there are 6 hours. A ship needs 8 meters of water depth. how long can it stay in the port...

Homework Statement A mass of 0.1 kg has 2 springs of length 20 cm attached to each side, like in the drawing. they are loose. one has a constant of 50 [N/m] and the other 30. The system is between 2 walls 10 cm distant from each spring. At the second stage the springs are tied each to the...

Q: When a sound wave with a certain intensity is detected by the tympanic membrane, the amplitude of the resultant motion is 1.0 nm (1.0 x 10-9 m). If the frequency of the sound is 600 Hz, what is the maximum speed of the membrane oscillation? My answer: 1)Vmax = wA (where w= angular velocity)...

Homework Statement A test was made with a basket and 20 gram weights. they were put in the basket which hang on a spring, the basket was raised and released. the period was measured for a few number of weights in the basket. the results are as follows. the first of every pair is the number of...

Hey PF, my book either got sloppy in a derivation or I am not connecting two very obvious dots. It gives the energy of the damped harmonic oscillator as E = (1/2)mv^2 + (1/2)kx^2 then takes the derivative with respect to time to get dE/dt. then it gives the differential equation of motion...

Hey guys, I'm reading the Theory of Sound and I've come to a part in which I'm having trouble double-checking the algebra. Suppose we have two harmonic sound waves of equal amplitude traveling directly perpendicular to each other. \begin{align} u=acos(2πnt-ε) && v=bcos(2πnt) \end{align} They...

Homework Statement I have to find a natural number N that satisfies this equation: \sum^{N}_{i=1} \frac{1}{i} > 100 Homework Equations I tried finding a close form of the sum but couldn't find anything useful. The Attempt at a Solution Well after trying some numbers in maple I...

Homework Statement Particle originally sits in ground state about x=0. Equilibrium is suddenly shifted to x=s. Find probability of particle being in new first excited state. Homework Equations The Attempt at a Solution Shifted wavefunctions are for ground state: ##\phi'_0 =...

Hello readers, Given the potential V(x) = - 1/ sqrt(1+x^2) I have found numerically 12 negative energy solutions Now I want to try to solve for these using matrix mechanics I know the matrix form of the harmonic oscillator operators X_ho, P_ho. I believe I need to perform the...

The energy changes correspond to infrared, h_bar * w. Which particles are actually oscillating? The neutrons or the electrons? Is it the electrons that fill up the stationary states, electronic configuration, or is it the nucleons that fill up the states?

A mass m slides on a frictionless horizontal surface, connected to two springs, as shown below. If the force have constants K1 and K2 , show that the simple harmonic sliding motion has period. T= 2 Pie (Square Root X m { K1+K2/K1K2}) So far I have →From equation T= 2Pie{SquareRoot(m/k)...

A simple harmonic oscillator has total energy E= ½ K A^2 Where A is the amplitude of oscillation.  E= KE+PE a) Determine the kinetic and potential energies when the displacement is one half the amplitude. b) For what value of the displacement does the kinetic energy equal the potential...

I am very familiar with the equation: $$f(t)=Asin(ωt+ϕ)$$ Used to describe the instantaneous value f(t) of a wave with amplitude A, frequency ω, and phase shift ϕ at time t. This equation is very intuitive to understand: As t increases the value within the sin operator will increase from ϕ...

Hi I have a damped simple harmonic motion model and I am altering the input force along with spring constant and damping constant. I can change the damping and spring constant to allow it to oscillate for few seconds before it stops at 0. What parameters do I need to change to alter the...

Homework Statement A yarn of material that cannot dilate, length L, mass m and elastic constant K is trapped and stretched with negligible tension between the two supports A and B attached to the ends of the metal bar, CD, whose coefficient of expansion varies linearly from to , increasingly...

Homework Statement A small sphere with mass m is attached to a massless rod of length L that is pivoted at the top, forming a simple pendulum. The pendulum is pulled to one side so that the rod is at an angle θ from the vertical, and released from rest. When the pendulum rod is...

Hi I am trying to model SHM in Simulink as shown here: http://pundit.pratt.duke.edu/wiki/Simulink/Tutorials/DiffEq I have tried using different values of spring constant and damping to get instant response to the input force. I am measuring the displacement calculated by SHM. The force changes...

Homework Statement 2N fermions of mass m are confined by the potential U(x)=1/2(k)(x2) (harmonic oscillator) What is the ground state energy of the system? Homework Equations V(x)=1/2m(ω2)(x2) The Attempt at a Solution I know the ground state energy of a simple harmonic...

Homework Statement a)Find a harmonic function ##u## on the annulus ##1< |z| < 2## taking the value 2 in the circle ##|z|=2## and the value 1 in the circle ##|z|=1##. b)Determine all the isolated singularities of the function ##f(z) = \frac{z+1}{z^3+4z^2+5z+2}## and determine the residue at...

Homework Statement A mass oscillates along the x-axis in simple harmonic motion. It goes through 200 cycles in 10 seconds and its vibrational amplitude is 0.020 m. What is the frequency, in hertz, and the total distance traveled, in meters, by the mass in the 200 cycles? Homework...

What means "harmonic"? The term "harmonic" arise in the math in several subjects, harmonic series, harmonic function, analysis harmonic, mean harmonic... but in each context harmonic have a different interpretation, but exist a general interpretation for "harmonic"? From where is "harmonic" and...

Homework Statement A particle is in simple harmonic motion with period T and with position as a function of time given by x(t) = A cos(wt+ø). At time t = 0 the particle is at x = A/2 with positive velocity. The next time it is at the same position is ___? Homework Equations...

Homework Statement A 2.00m long rope is stretched between two supports with a tension that makes the speed of transverse waves 48.0m/s . What are the wavelength of the second overtone? Homework Equations L=nλ/2 The Attempt at a Solution I got 2.00 m. Since L=2.00m and n=2 being the 2nd...

Homework Statement A mass of 0.4 kg, hanging from a spring (k= 80N/m) is set into an up-and-down SHM. What is the speed of the mass when moving through the equilibrium point? The starting displacement, A, is 0.10 m. Homework Equations a = -kx/m ω = 2pi/TThe Attempt at a Solution I tried to...

Homework Statement I have 2 simple harmonic motions and I want to compose them on the same axis. So: x1 = A1*sin(ω1*t+θ1) x2 = A2*sin(ω2*t+θ2) The goal is to find the resultant motion of these 2 in the form: X = A*sin(ω*t+Θ), so to find A,ω and Θ as functions of A1,A2,ω1,ω2,θ1 and...

Homework Statement Part (a): Derive Ehrenfest's Theorem. What is a good quantum number? Part (b): Write down the energy eigenvalues and sketch energy diagram showing first 6 levels. Part (c): What's the symmetry of the new system and what happens to energy levels? Find a new good quantum...

Homework Statement The function x = (7.4 m) cos[(5πrad/s)t + π/5 rad] gives the simple harmonic motion of a body. At t = 6.2 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion...

Problem: Show that the combined spring energy and gravitational energy for a mass m hanging from a light spring of force constant k can be expressed as 1/2 ky2, where y is the distance above or below the equilibrium position. Figure shows a block connected to spring, where equilibrium is...

Homework Statement I was wanting to get some clarification on some of the simple harmonic motion equations. So, say for example there is a box of mass "m" undergoing simple harmonic motion attached to a spring of spring constant K on a horizontal surface. To find where the box is, as a...

Homework Statement a small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is the same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such that the small mass is at the top. Find the least R/r ratio such that the...

In the course of solving the simple harmonic oscillator, one reaches a fork in the road. x(t) = A1Sin(wt) + A2Cos(wt) At this point, you exploit a trig identity and arrive at one of two solutions x(t) = B1Sin(wt+phi1) or x(t) = B2Cos(wt+phi2) Both of these are correct solutions...

The nonlinear oscillator $y'' + f(y)=0$ is equivalent to the Simple harmonic motion: $y'= -z $, $z'= f(y)$ the modified Symplectic Euler equation are $$y'=-z+\frac {1}{2} hf(y)$$ $$y'=f(y)+\frac {1}{2} hf_y z$$ and deduce that the coresponding approximate solution lie on the family of curves...

Given the equations for the harmonic oscillator $\frac{dy}{dz}=z, \frac{dz}{dt}= -y$if the system is approximated by the symplectic Euler method, then it gives$z_{n+1}= z_{n}-hy_{n}, \\ y_{n+1}= y_{n}+hz_{n+1}$which shows that the circle $y^2_{n} + z^2_{n} = 1$ is mapped into an ellipse...

Homework Statement An object moving with harmonic motion has an acceleration of -2 m/s^2 when the elongation is 0.5 m. Determine the angular frequency and the velocity and acceleration for t=1s. Homework Equations a=-ω2x (1) x=Acos(ωt+θ) (2) a=-Aω2cos(ωt+θ) (3) The Attempt at a...

Hi folks! Apparently \Psi(x) = Ax^ne^{-m \omega x^2 / 2 \hbar} is an approximate solution to the harmonic oscillator in one dimension -\frac{\hbar ^2}{2m} \frac{d^2\psi}{dx^2} + \frac{1}{2}m \omega ^2 x^2 \psi = E \psi for sufficiently large values of |x|. I thought this...

Edit: Problem solved please disregard this post Homework Statement A particle in the harmonic oscillator potential has the initial wave function \Psi(x, 0) = ∑(from n = 0 to infinity) Cnψn(x) where the ψ(x) are the (normalized) harmonic oscillator eigenfunctions and the coefficients are given...

Hi I am using Simple Harmonic Motion in a Matlab/Simulink model. Instead of using a motion for a simple pendulum, I decided to use a spring with a mass. The reasons for this is because my example is more like a lever attached to a pivot point and having an object at the end with a mass. A...

Homework Statement A particle moves along the x axis. It is moving initially at the position 0.280 m, moving with velocity 0.200 m/s and acceleration -0.450 m/s^2. Suppose it moves with constant acceleration for 4.10 s. (a) Find the position of the particle after this time...

Homework Statement Hi, so my question is about a damped simple harmonic motion experiment The experiment is as follows: A 30 cm ruler with a needle attached to it is clamped to a bulldog clamp. The needle is placed in a beaker of water so that it is just inside the water ( by about...

Homework Statement I found this in Binney's text, pg 154 where he described the radial probability density ##P_{(r)} \propto r^2 u_L## Homework Equations The Attempt at a Solution Isn't the radial probability density simply the square of the normalized wavefunction...

The problem is a ball is dropped onto a spring and the spring compresses .95m. The ball then sticks to the spring and oscillates with a period of 1.1 seconds and has a mass of 6kg. I thought that the equation mg(h+x)=1/2(k)(x^2) would be what i would use. I got h=.47m I also...

I'm trying to plot the evolution of a simple harmonic oscillator using MATLAB but I'm getting non-sense result and I have no idea what's wrong! Here's my code: clear clc x(1)=0; v(1)=10; h=.001; k=100; m=.1; t=[0:h:10]; n=length(t); for i=2:n F(i-1)=-k*x(i-1)...

Homework Statement A particle of mass m moves in a 1-D Harmonic oscillator potential with frequency \omega. The second excited state is \psi_{2}(x) = C(2 \alpha^{2} x^{2} + \lambda) e^{-\frac{1}{2} a^{2} x^{2}} with energy eigenvalue E_{2} = \frac{5}{2} \hbar \omega. C and \lambda are...