Harmonic Definition and 1000 Threads

Homework Statement [/B] For differential equation of the form ## y''- y = 0 ## BC is ## y(1) = B ## which usually have general solution ## y(x) = C1 e^x + C2 e^{-x} ## But this manual I am reading always want to go with general solution ## y = C1 \cosh(x) + C2 \sinh( x) ## I assume...

Homework Statement A particle is moving in a 1-dimensional harmonic osciallator with the hamiltion: ## H = \hbar \omega (a_+ a_- + \frac{1}{2})## at time ## t=0## the normalized wave function is given by ## \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x) + i\psi_1(x)) ## Task: Calculate for ## t \geq...

In school we have numerous exercises that ask you to find the time when a body passes a certain point for the nth time in simple harmonic oscillation. But it is a bit mentally taxing to solve with the actual formula of x=Asin(ωt + φ), just because you have to sort out all the infinite solutions...

Homework Statement A particle is moving in a one-dimensional harmonic oscillator, described by the Hamilton operator: H = \hbar \omega (a_+ a_- + \frac{1}{2}) at t = 0 we have \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x)+i\psi_1(x)) Find the expectation value and variance of harmonic oscillator...

Homework Statement on page 51 (of my book, probably not current) section 2.3.2 equation 2.74 and 2.75 d2ψ / dξ2 ≈ ψξ2 Homework Equations This is an approximation of the Schrodinger equation with a variable introduced ξ = √(mω/h) The solution is given: ψ(ξ) = Ae-ξ2/2 +Beξ2/2The Attempt at...

Homework Statement An un-damped harmonic oscillator natural frequency ##\omega_0## is subjected to a driving force, $$F(t)=ame^{-bt}.$$ At time, ##t=0##, ##x=\dot{x}=0##. Find the equation of motion. Homework Equations ##F=m\ddot{x}## The Attempt at a Solution We have...

Homework Statement Reading chapter 4 of Morin's "Introduction to classical mechanics" I came across to the explanation of the damped harmonic motion. The mass m is subject to a drag force proportional to its velocity, ##F_f = -bv ##. He says that the total force of the mass is ##F= -b \dot{x}...

Homework Statement Answer: Can someone explain the answer? I don't understand why it's necessary for that the moment when the force exerted on the smaller block is greatest is when it is on the verge of slipping. Could it not already have been slipped off or maybe even 3/4 way slipped off...

Homework Statement Consider an inertial laboratory frame S with coordinates (##\lambda##; ##x##). The Lagrangian for the relativistic harmonic oscillator in that frame is given by ##L =-mc\sqrt{\dot x^{\mu} \dot x_{\mu}} -\frac {1}{2} k(\Delta x)^2 \frac{\dot x^{0}}{c}## where ##x^0...

Homework Statement Two positive point charges Q are located at points (±l, 0). A particle with positive charge q and mass m is initially located midway between them and is then given a tiny kick. If it is constrained to move along the line joining the two charges Q, show that it undergoes...

Homework Statement Homework Equations ##\tau = rFsin(\theta)## ##\tau_{net} = I\alpha## ##F = -kx## ##kx = mg## The Attempt at a Solution I don't understand how the restoring force from the bending of the ruler behaves (so I have no idea how to apply torque here). I also don't understand how...

Hi, I have been looking in various text about how to find an admissible solution to the Schrödinger eqn in one dim. in the harmonic oscillator model. As in MQM, the solutions to this are said to be ##Ae^{ikx}+Be^{-ikx}##, which are then said to be not admissible. The book then goes straigtht to...

One thing I don't understand is that How Amplitude is conserved on both sides if the mass is subjected to different forces on either side of this shm...

$$m_1 \ddot{x} - m_1 g + \frac{k(d-l)}{d}x=0$$ $$m_2 \ddot{y} - m_2 \omega^2 y + \frac{k(d-l)}{d}y=0$$ It is two masses connected by a spring. ##d=\sqrt{x^2 + y^2}## and ##l## is the length of the relaxed spring (a constant). What is the strategy to solve such a system? I tried substituting...

Homework Statement A simple harmonic oscillator, with oscillations in the x direction, has velocity given by: $$v_{x} = (2.2 \frac {\mathrm{m}} {\mathrm{s}}) \sin [(6.9 \frac {\mathrm{rad}} {\mathrm{s}}) t]$$. Find the values of ##\omega , A, f , T ,## and ##\phi## Homework Equations $$v_{x} =...

Homework Statement A perfectly solid marble of radius R rolls without slipping at the bottom of a spherical bowl of a radius 6R. The marble rolls back and forth in the vertical plane executing simple harmonic motion close to the lowest point. How long does it take the marble to go down one side...

Homework Statement the cone of a loudspeaker vibrates in SHM at frequecy of 262Hz. the amplitude at the center of the cone is A=1.5X10^-4m and t=0 and x=A (amplitude). 1) what equation describes the motion of the center of the cone ? 2) what are the velocity and acceleration as a function of...

I have some difficulties in viewing the literature on the topic. In textbooks on analytical mechnics the procedure given for Special relativistic motion is to write the kinetic term relativistically and attach the unchanged potential term. So, for a harmonic oscillator the Lagrangian is ##L =...

I have a spring with mass M attached, and leave it at equilibrium. Then I displace it some more by stretching it down a bit more. Displacement due to the mass= X, displacement due to stretching it even more=Y. Why isn't the amplitude of oscillation= X+Y, but is only actually only Y? This is...

Homework Statement If the first two energy eigenfunctions are ## \psi _0(x) = (\frac {1}{\sqrt \pi a})^ \frac{1}{2} e^\frac{-x^2}{2a^2} ##, ## \psi _1(x) = (\frac {1}{2\sqrt \pi a})^ \frac{1}{2}\frac{2x}{a} e^\frac{-x^2}{2a^2} ## Homework EquationsThe Attempt at a Solution Would it then be...

Homework Statement [/B] For the first excited state of a Q.H.O., what is the probability of finding the particle in -0.2 < x < 0.2 Homework Equations Wavefunction for first excited state: Ψ= (√2) y e-y2/2 where: The Attempt at a Solution To find the probability, I tried the integral of...

I saw a question "If you blow across the open end of a soda bottle and produce a tone of 250 Hz, what will be the frequency of the next harmonic heard if you blow much harder?" the answer is 750 Hz but I'm curious about "if you blow much harder" part, is it really depends on how much harder...

1. Homework Statement I've been using a recurrence relation from "Adv. in Physics"1966 Nr.57 Vol 15 . The relation is : where Rnl are radial harmonic oscillator wave functions of form: The problem is that I can't prove the relation above with the form of Rnl given by the author(above). I've...

I'm currently studying IR but my mind is having trouble tying everything together. While I see that vibrational frequency is determined really by just reduced mass, I can see from the equation that vib equation is the same throughout energy levels and so does energy (bc that basically depends...

Homework Statement I don’t have a specific problem to solve, and I’m not sure I would be able to correctly find one, but I need to know how to solve a harmonic Oscilator problem with Friction. I believe I should be starting with F = -kx -Ff, and that I will be given some information about the...

I am very confused about angular velocity ω and why its used in simple harmonic motion. ω is described as θ/τ but when it comes to masses on springs, there is no angle - it is zero. Angular velocity comes from circular motion but the motion of SHM is not circular. My confusion is even greater...

See attached photo please. So, I don't get how equations of motion derived. Why is it that x dot is partial derivative of H in term of p but p dot is negative partial derivative of H in term of x.

Homework Statement https://drive.google.com/file/d/0Byoif068nH-zWTNHQTJid0gxRm8/view?usp=sharing[/B] x=0.05m v=2m/s w=10 rad/s Find the simple harmonic equation. Homework Equations x(t)=A sin (wt+psi) conservation energy The Attempt at a Solution use conservation of energy to find...

Homework Statement Show that the virial theorem holds for all harmonic-oscillator states. The identity given in problem 5-10 is helpful. Homework Equations Identity given: ∫ξ2H2n(ξ)e-ξ2dξ = 2nn!(n+1/2)√pi P.S the ξ in the exponent should be raised to the 2nd power. So it should look like ξ2...

Homework Statement Show that application of the lowering Operator A- to the n=3 harmonic oscillator wavefunction leads to the result predicted by Equation (5.6.22). Homework Equations Equation (5.6.22): A-Ψn = -iΨn-1√n The Attempt at a Solution I began by saying what the answer should end...

Homework Statement The point of the needle of a sewing machine moves in SHM along the x-axis with a frequency of 2.5 Hz. At t=0 its position and velocity components are +1.1 cm and -15 cm/s, respectively. (a) Find the acceleration component of the needle at t=0 (b) write an equation giving the...

Homework Statement A spring holds a weight of 800 g. The spring is set in a harmonious swing. The frequency f for the oscillation is 1.4 Hz. When the weight is 5 cm above the equilibrium position on the way upwards, a velocity of 1.1 m / s is noted a) Determine the amplitude of the movement. b)...

Hi again, got a few questions (marked with numbers) for passive filters used to filter harmonic currents in the power system. Look at my one-line diagram below. Let's say I have a passive filter connected in shunt with respect to the load and the passive filter "diverts" the harmonic currents...

Homework Statement This is a question asked in a entrance examination[/B] A charged particle is in the ground state of a one-dimensional harmonic oscillator potential, generated by electrical means. If the power is suddenly switched off, so that the potential disappears, then, according to...

Homework Statement Homework EquationsThe Attempt at a Solution I know that when displacement is max, kinetic energy is 0 and when displacement is o, kinetic energy is max and I know is should always be above the axis because KE can't be negative But what about the amplitude and frequency...

One of the conditions to distinguish Simple Harmonic Motion from other harmonic motions is by the relation that a∝x where x is the displacement from the point that acceleration is directed towards But what confuses me is the constant of proportionality introduced to this relation: ω2 ω is...

A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that. However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation. And then there are words like: harmonics (for higher...

Homework Statement Consider a Simple Harmonic Motion (SHM) for which, at time t = 1 s, the displacement is s=1 cm, the velocity is 2 cm s−1, and the acceleration is −3 cm s−2. Find the angular frequency, 4. amplitude, and phase constant for this motion. Homework Equations f=1/T...

If you consider b^2/m > 4*k, you can get the solution by using classic method (b = damping constant, m = mass and k = spring constant) otherwise you have to use complex numbers. How have the references books proved the solution for this differential equation?

Homework Statement An undamped harmonic oscillator (b=0) is subject to an applied force Focos(wt). Show that if w=wo, there is no steady- state solution. Find a particular solution by starting with a solution for w=wo+#, and passing to the limit #->0, it will blow up. Try starting with a...

Hi Q1: I was reading about ultraviolet catastrophe and it was said that atoms were assumed to be harmonic oscillators of radiation. I believe that two harmonic oscillators could have the same frequency but different amplitudes so it would mean that two different atoms (i.e. two harmonic...

Homework Statement I am currently reading a textbook on solving the Schrödinger equation for the harmonic oscillator using the series method; $$-\frac{\hbar^{2}}{2m}\frac{\mathrm{d}^2 \psi }{\mathrm{d} x^2}+\frac{1}{2}m\omega ^{2}x^2\psi =E\psi $$ It starts by using these two dimensionless...

1. A mass, M = 1.61 kg, is attached to a wall by a spring with k = 559 N/m. The mass slides on a frictionless floor. The spring and mass are immersed in a fluid with a damping constant of 6.33 kg/s. A horizontal force, F(t) = Fd cos (ωdt), where Fd = 52.5 N, is applied to the mass through a...

I started to ponder following problem. I have a driven, damped oscillator where the mass is free to vibrate in y-direction. If I put a wall or a ground near the mass, the mass touches it if the drive amplitude is larger than the distance to the ground. How does this change the normal dynamics. I...

Homework Statement Two particles move parallel to the x-axis about the origin with the same amplitude and frequency. At a certain instant, they are found at a distance A/3 from the origin, on opposite sides of the origin, with their velocities in the same direction. Find the phase difference...

Hi everyone, I have a great doubt in this problem: Let a mass m with spin 1/2, subject to the following central potencial V(r): V(r)=1/2mω2r2 Find the constants of motion and the CSCO to solve the Hamiltonian? This is my doubt, I can't find the CSCO in this potencial. Is a problem in general...

Hi, Out of interest, today I was mucking around with a 160W LED, 240V, 50hz, outdoor light. I looked at the Power Factor (it was 0.96) and the THD was 14.something %. I then wondered what would happen if I put a capacitor in parallel with the light. It was a three phase 90uF cap, so since they...

Homework Statement In Griffiths' book "Introduction to Quantum Mechanics", Section 2.3, Chapter 2, the Fig. 2.7 gives the plots of the wave function (##\psi_{n}##) and its modulus of the harmonics oscillator, see the Appendix. With the order (##n##) increasing, they become both higher. However...

Homework Statement The problem: The mass the m is placed on the rod with the bushing remaining stationary. The end of the rod deflects 2 cm. The bushing is then given a vertical motion y(t) = 0.4 sin (20t) cm. Determine the magnitude of the motion of the mass m (either relative to the bushing...

Homework Statement I do not fully grasp the concept behind all of these sub questions (i)-(iv). Homework Equations v=wAcos(wt) (SMH)? Friction Force = Coefficient of Friction * Normal Force The Attempt at a Solution (i) Varying as simple harmonic motion sees varying acceleration as it...