Harmonic Definition and 1000 Threads

Homework Statement Hi everybody! I'm a bit stuck in this problem, hopefully someone can help me to make progress there: A mass point ##m## is under the influence of a central force ##\vec{F} = - k \cdot \vec{x}## with ##x > 0##. a) Determine the equation of motion ##r = r(\varphi)## for the...

I think I miss something about energy of a mechanical wave. In absence of dissipation the mechanical energy transported by an harmonic wave is constant. $$E=\frac{1}{2} A^2 \omega^2 m$$ But, while studying normal modes on a rope, I find that the mechanical energy of a normal mode (still...

Homework Statement A particle of mass 0.50 kg performs simple harmonic motion along the x-axis with amplitude 0.55m and period 4.3 seconds. The initial displacement of the particle is -0.30 m and it is traveling in the positive x-direction. The phase constant of the motion (Φ) = -2.15 rad...

Here is the new thread. Please justify your criticism of my statement.

Homework Statement A body performaning simple harmonic motion has a displacement x given by the equation x= 30 sin 50t, where t is the time in seconds. what is the frequency of the oscillation? Answers are: A. 0.020Hz B. 0.13Hz C. 8.0Hz D. 30Hz E. 50Hz (correct...

Homework Statement I need to find a way to do a conversion between the angular motion of a motor to the angular motion of an oscilating bar that is connected to it through a sliding and rotating collar. This way, every time the motor completes a revolution, the bar swings back and forth with a...

Homework Statement Homework Equations None. The Attempt at a Solution Hi everyone. Apparently 5 is the right answer, although I chose D. Could anyone please weigh in with their thoughts about why 5 is right and my answer is apparently wrong? Thanks!

Homework Statement I am supposed to calculate Lyapunov exponent of a damped, driven harmonic oscillator given by ## \ddot{x} + 2\beta \dot{x} + \omega_0^2 x = fcos(\omega t)## Lyapunov exponent is ## \lambda ## in the equation ## \delta x(t) = \delta x_0 e^{\lambda t} ## The attempt at a...

Homework Statement Hello, folks:) I'm currently having problem with properly understanding the difference and aplications of two equations which resemble each other greatly, but the difference makes it difficult for me to tell exactly which one is for what. 2. Homework Equations Those two...

Homework Statement In the figure, block 2 of mass 2.40 kg oscillates on the end of a spring in SHM with a period of 26.00 ms. The position of the block is given by x = (1.80 cm) cos(ωt + π/2). Block 1 of mass 4.80 kg slides toward block 2 with a velocity of magnitude 6.90 m/s, directed along...

Homework Statement Two particles oscillate in simple harmonic motion along a common straight-line segment of length 1.5 m. Each particle has a period of 1.5 s, but they differ in phase by π/5 rad. (a) How far apart are they 0.46 s after the lagging particle leaves one end of the path? (b) Are...

Homework Statement Show that the partition function for the harmonic oscillator with an additional force H = \hbar \omega a^{\dagger} a - F x_0 (a + a^{\dagger}) is given by \frac{e^{\beta \frac{F^2 x_{0}^2}{\hbar \omega}}}{1-e^{\beta \hbar \omega}} and calculate \left<x\right> = x_0...

Homework Statement This problem is a continuation of the problem I posted in this thread: https://www.physicsforums.com/threads/equation-of-motion-from-a-lagrangian.867784/ (We have set the mass per unit length in that question to ##\sigma## = 1 to simplify some of the formulae a little.)...

Homework Statement On June 10, 2000, the Millennium Bridge, a new footbridge over the River Thames in London, England, was opened to the public. However, after only two days, it had to be closed to traffic for safety reasons. On the opening day, in fact, so many people were crossing it at the...

Homework Statement A uniform rod of mass m and length L is freely pivoted at one end. What is the period of its oscillations? Icm for a uniform rod rotating about its centre of mass is 1/12mL2 (a) √3g/2L (b) 2π √3L/2g (c) 2π √2L/3g (d) 2π √L/g (e) none of the above Homework Equations ω2 =...

Hello, I have the solution of a problem but there's something I don't understand Homework Statement Find the harmonic function in the square {0<x<1, 0<y<1} with the boundary conditions u(x,0)=x u(x,1)=0 ux(0,y)=0 ux(1,y)=y²tHomework EquationsThe Attempt at a Solution Part1:[/B] We first solve...

Homework Statement A 12.0-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)=4.50cmcos[(19.5s−1)t−π/8]. (a) What is the spring constant of the spring? (b) What is the maximum...

Hi. As far as I know, the movement of a harmonic oscillator normally is not considered to be chaotic. Why not? Since the angular frequency can never be known to absolute precision, an error in the phase builds up. I can see that this build-up is only linear in time (if we assume the angular...

Homework Statement A 0.61 kg mass attached to a spring (k = 27 N m-1) is performing SHM on a smooth horizontal surface. Calculate the periodic time of these oscillations. Homework Equations ω=2π/T ω=2πƒ The Attempt at a Solution I think I need to find out the angular frequency ω of the...

where ##□=\nabla^{\mu}\nabla_{\mu}## is the covariant D'Alembertian. ##□x^{\mu}=0## ##g^{\rho\sigma}\partial_{\rho}\partial_{\sigma}x^{\mu}-g^{\rho\sigma}T^{\lambda}_{\rho\sigma}\partial_{\lambda}x^{\mu}=0## So this line is fine by subbing in the covariant derivative definition and lowering...

Homework Statement i know that k = 0 to∞∑(1/ k) is harmonic series( we know that the sum is divergent) , how about ∑(1/ k+1 ) ? Homework EquationsThe Attempt at a Solution in my opinion , it's also harmonic series , because the sum is divergent . Am i right ?

For the lab I have to find the spring constant and how force relates to time with simple harmonic motion. To find the spring constant, I used hooke's law and compared different added masses to the stretch from the equilibrium position. When I graphed that, the slope was the spring constant since...

Homework Statement Point with mass is moving along the positive direction of x axis, its velocity is described by (A-Bx^2)^(1/2). Show that its equation of motion describes dynamic harmonic oscillation and find period (T) of this oscillation. Homework Equations v=(A-Bx^2)^(1/2) A and B is...

Homework Statement Homework Equations Find Time Period. Find the error in my solution. The Attempt at a Solution Where i am wrong ?

So I was just trying to differentiate (for no good reason) the equation : x=x0sin(wt) (w= angular frequency, x0= maximum displacement, t=time) to obtain the expression : a= -w2x I differentiated twice with respect to time the initial expression for x and got: a= -w2x0sin(wt) I must have...

Homework Statement Two particles are executing simple harmonic motion of the same amplitude A and frequency ω along the x-axis. Their mean position is separated by distance X0 (X0 > A). If the maximum separation between them is (X0 + A), the phase difference between their motion is My answer...

Homework Statement Consider a particle with mass m oscillates in a simple harmonic potential with frequency ω. The position, x, and momentum operator, p, of the particle can be expressed in terms of the annihilation and creation operator (a and a† respectively): x = (ħ/2mω)^0.5 * (a† + a) p =...

Homework Statement Spring with spring constant k=2000N/m has an object with mass 10kg attached to it. When it is pulled 0.1m away from the equilibrium state it starts oscillating and came to a stop. The coefficient of kinetic friction is 0.2 and the coefficient of static friction is 0.5. Find...

Homework Statement A pendulum swings at 70 cycles per minute. a. What is the frequency in Hz? b. What is the period in seconds? Homework Equations T = 1 / f The Attempt at a Solution For part a) Used the answer for part b & I took the equation above, divided 1 by 1.167 cycles/second & got...

Homework Statement consider any damped harmonic oscillator equation m(d2t/dt2 +bdy/dt +ky=0 a. show that a constant multiple of any solution is another solution b. illustrate this fact using the equation (d2t/dt2 +3dy/dt +2y=0 c. how many solutions to the equation do you get uf you use this...

Hi, why there is only odd eigenfunctions for a 1/2 harmonic oscillator where V(x) does not equal infinity in the +ve x direction but for x<0 V(x) = infinity. I understand that the "ground state" wave function would be 0 as when x is 0 V(x) is infinity and therefore the wavefunction is 0, and...

Homework Statement Due to the radial symmetry of the Hamiltonian, H=-(ħ2/2m)∇2+k(x^2+y^2+z^2)/2 it should be possible to express stationary solutions to schrodinger's wave equation as eigenfunctions of the angular momentum operators L2 and Lz, where...

Homework Statement Part d) of the question below. Homework Equations We are told NOT to use the ladder technique to find the position operator as that's not covered until our Advanced Quantum Mechanics module next year (I don't even know this technique anyway). I emailed my tutor and he...

Question: The frequencies of the first three harmonics of a 300 Hz square wave are 300 Hz, 900 Hz, and 1500 Hz. If the amplitude of the fundamental is 1.00 A, then the amplitudes of the second harmonic is _____ A, and the amplitude of the third harmonic is _____ A. I found the answer to the...

Homework Statement A guitar player is plucking a strong of length 30cm. How fast must the player move towards or away from the stationary observer, in order for the observer to mistake the fundamental frequency for the second harmonic? ANSWER: 2(Vsound) towards the observer Homework...

Homework Statement As the captain of the scientific team sent to Planet Physics, one of your tasks is to measure g. You have a long, thin wire labeled 1.80 g/m and a 1.30 kg weight. You have your accurate space cadet chronometer but, unfortunately, you seem to have forgotten a meter stick...

Homework Statement The periodic motion is given in the form: f(t) = Acos(wt+φ) What is the amplitude and phase constant for the harmonic oscillator when: (a) f(t) represents position function x(t) (b) f(t) represents velocity function v(t) (c) f(t) represents acceleration function a(t)...

Homework Statement The wave function for the three dimensional oscillator can be written ##\Psi(\mathbf r) = Ce^{-\frac{1}{2}(r/r_0)^2}## where ##C## and ##r_0## are constants and ##r## the distance from the origen. Calculate a) The most probably value for ##r## b) The expected value of ##r##...

So this is something that troubled me a bit- in Shankar's PQM, there's an exercise that asks you to find the position expectation value for the harmonic oscillator in a state \psi such that \psi=\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle) Where |n\rangle is the n^{th} energy eigenstate of...

Homework Statement Homework EquationsThe Attempt at a Solution I'm working on part a. The numerical value of Q. I have an equation stating that Q = ω_0/ϒ. I don't really know what ϒ is, in other places (http://farside.ph.utexas.edu/teaching/315/Waves/node13.html) it seems like the...

For a 1D QHO we are given have function for ##t=0## and we are asked for expectation and variance of P at some time t. ##|\psi>=(1/\sqrt 2)(|n>+|n+1>)## Where n is an integer So my idea was to use Dirac operators ##\hat a## and ##\hat a^\dagger## and so I get the following solution ##<\hat...

Homework Statement The problem is attached Homework Equations f=2π/ω=2π√(m/k) The Attempt at a Solution My idea is that the mass doubles resulting in a √2 increase in the equation above. However, apparently the answer is (c). I have a strong feeling the book answer is wrong, but I wanted to...

Given a Simple Harmonic Progressive Wave with the equation y=A*sin(ωt-kx+φ) where A is amplitude, k is wave number, ω is frequency of wave and φ is the initial phase. How to determine in what direction is the wave propagating?

Homework Statement Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad/s, and amplitude 1.6 cm while the bigger mass remains stationary on the ground. The maximum force...

Homework Statement The amplitude of a simple pendulum oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes Law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of...

I know the phase constant depends upon the choice of the instant t=0. Is it compulsory that the phase constant must be between [0,2π] ? I know that after 2π the motion will repeat itself so it will not really matter, but what is the conventional way to write the phase constant in the general...

Homework Statement A particle with a mass(m) of 0.500kg is attached to a horizontal spring with a force constant(k) of 50.0N/m. At the moment t=0, the particle has its maximum speed of 20m/s and its moving to the left. Find the minimum time interval required for the particle to move from...

When I work out $$b^+b$$, I get $$\widehat{b^+} \widehat{b} = \frac{1}{2} (ξ - \frac{d}{dξ})(ξ + \frac{d}{dξ}) = \frac{1}{2} (ξ^2 - \frac{d^2}{dξ^2}) = \frac{mωπx^2}{h} - \frac{h}{4mωπ} \frac{d^2}{dx^2}$$ So base on what I have about, (9) should be $$(9) = \frac{hω}{2π} (\frac{1}{2}...

If you haven't seen this video before then go watch it :D Question: Answer: It is pretty hard to imagine it as a spring and here is why: 1) At (o) the spring should move by its inertia not by any force. If we look at the planet we can summarize that there are 2 points (As I think) that could...

I found an explanation for the equation of under damped harmonic motion, x(t) = C cos(wt) + D sin(wt), but I was wondering if someone could further explain why: - "However, if you assume the function x(t) is real, then they are related as A = B - why is (A-B) is imaginary