Harmonic Definition and 1000 Threads

All Questions are shown on pictures. My Calculated answers: A1(a) R= 19.21∠68.7o N (b) E = 19.21∠-111.34o N or = -19.21∠68.7o N <--- Is't either one answer is correct or not? If not, which answer is correct and why? Thanks. A2(b) I = 0.5mr2 = 1.125kgm2 A2(a) k=(I/m)1/2 = 0.212m...

Hello. I have a tiny question that has confused me. Currently I'm reading about potential wells, harmonic oscillators, the free particle in quantum physics. If I just take the particle in a box as an example you have a region where the potential is zero, and you have some walls/boundaries...

Homework Statement Homework Equations The Attempt at a Solution for part a I do not know how to write it in power series form ? for part b : I chose the perturbed H' is v(x)= (1+ε )K x^2 /2 then I started integrate E_1 = ∫ H' ψ^2 dx the problem was , the result equals to ∞ ! shall I...

[b]1. The motion of a forced harmonic oscillator is determined by d^2x/dt^2 + (w^2)x = 2cos t. Determine the general solution in the two cases w = 2 and w is not equal to 2. To be honest I've no idea where to start!

Hi friends the problem is - https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/s480x480/155412_2656530589803_1383873256_n.jpg Attempt - As per the problem states, When the compound system will oscillate in its natural frequency, The frequency of the oscillation will be, √[k/(m...

Hi friends the problem is - https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/s480x480/60061_2656517749482_1458399262_n.jpg Attempt - As per the problem states, The net force on the particle will be ...

Hi friends the problem is - https://fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-ash4/430884_2656507629229_1511525381_n.jpg Attempt - friend as per the question I am trying to get structure of SHM, The displacement equation x = A sin(ωt + θ) represents SHM where ωt + θ is Phase of the...

Hi friends the problem is - https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/30370_2656498989013_1471109032_n.jpg Attempt - friends as per the question I am trying to get the acceleration- displacement equation for this problem. So I am using F = - (dU / dx)...

Hi friends the problem is - https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-snc6/s480x480/6405_2656465868185_1414230035_n.jpg Attempt - As per the problem states, For the first second equation of SHM, (using x = A sin ωt) a = A sin ω From here I get, sin ω = a/ A...

Homework Statement The two linear simple harmonic motions of equal amplitudes , and angular frequencies ω and 2ω are imposed on a particle along the axes of X and Y respectively. If the initial phase difference between them is π/2 , then find the resultant path followed by the particle...

Hi All, If there is something fundamentally wrong in my understanding of quantum mechanics, pardon me for I have just started learning it. We know that if we can come up with a solution for Schrodinger Equation of a Harmonic Oscillator, then we can generate further solutions by acting on it...

I've been looking around and trying to figure it out, but I can't seem to figure out how the cosine function get's into the solution to the HO equation d2x/dt2=-kx/m. I know this is extremely basic, but could someone indulge me?

Homework Statement This is a 3 part problem and I've successfully solved the first 2 parts, but I don't know what I did wrong in the third part. 1) mass of 346 g on a spring with constant 26.8 N/m on a horizontal + frictionless surface. Amplitude is 6.7 cm. In part 1 i found the total...

Hi Can someone please explain the answer to the following thread? I tried uncoupling the Hamiltonian but to no avail. https://www.physicsforums.com/showthread.php?t=602106 Thank you.

A particle has its wave function as the ground state of the harmonic oscillator. Suddenly the spring constant doubles (so the angular frequence dobules). Find the propability that the particle is afterwards in the new ground state. I did solve this, it was quite easy. But doing so I encountered...

Homework Statement The generalization of the bohr rule to periodic motion more general than circular orbit states that: ∫p.dr = nh = 2∏nh(bar). the integral is a closed line integral and the bolded letters represent vectors. Using the generalized, show that the spectrum for the...

Homework Statement At time t < 0 there is an infinite potential for x<0 and for x>0 the potential is 1/2m*w^2*x^2 (harmonic oscillator potential. Then at time t = 0 the potential is 1/2*m*w^2*x^2 for all x. The particle is in the ground state. Assume t = 0+ = 0- a) what is the probability that...

Homework Statement I'm doing a lab, and they want me to show the dependence of the period on different variables (displacement, mass, and length of pendulum). They ask me to "Fit curves to your plots to show the dependence. Use the curve fits from your plots to devise an equation for...

at the extreme position, the restoring force that developed, is it's magnitude more than the initial force imparted? and that's why it goes back to the mean position or is it that, the magnitude is same and it just goes back to attain stable equilibrium?.

Homework Statement The harmonic mean of the roots of the equation (5+\sqrt{2})x^2-(4+\sqrt{5})x+8+2\sqrt{5}=0 Homework Equations The Attempt at a Solution I know this question is easy but the main problem arises in finding the roots of the above equation. When I use the quadratic...

Homework Statement A machine part is undergoing SHM with a frequency of of 5hz and amplitude of 1.80cm. How long does it take the part to go from x = 0 to -1.80cm? Homework Equations x = Acoswt The Attempt at a Solution X is given and convert it to metres 0.018. I need to...

So, this has been bothering me for a while. Lets say we have the wavefunction of a harmonic oscillator as a general superposition of energy eigenstates: \Psi = \sum c_{n} \psi _{n} exp(i(E_{n}-E_{m})t/h) Is it true in this case that <V> =(1/2) <E> . I tried calculating this but i...

Homework Statement A 93-kg box hangs from the ceiling of a room—suspended from a spring with a force constant of 540 N/m. The unstressed length of the spring is 0.505 m. (a) Find the equilibrium position of the box. (b) An identical spring is stretched and attached to the ceiling and the box...

Homework Equations I do not why the particle does the simple harmonic motion. And how to find such innitial condition to satify r decreases continually in time. [b]3. The Attempt at a Solution [/b Is it need to take derivative of r?

Homework Statement I have a question pertaining to the simple harmonic motion of the midpoint of a guitar string with a frequency of 4.40 x 10^2 Hz and an amplitude of 1.60 mm. I've been asked to deduce the initial displacement, velocity and acceleration of the midpoint of the string, but am a...

I had a lecture regarding harmonic motion. he also derived equation related to pendulum motion with extended object and equation is following.(motion is a simple harmonic motion) d^2θ/dt^2+(RcmMg)θ/I=0 θ(t) = θcos(Ωt)+(ω/Ω)sin(Ωt) where Ω is defined angular frequency oscillation for all...

Homework Statement Use the following trial function: \Psi=e^{-(\alpha)r} to estimate the ground state energy of the central potential: V(r)=(\frac{1}{2})m(\omega^{2})r^{2} The Attempt at a Solution Normalizing the trial wave function (separating the radial and spherical part)...

Homework Statement I was being asked to find the limitation and possible ways to improve the following experiment Cantilever experiment to record the time of fixed oscillations as the length of the ruler with a fixed mass increases each time. The Attempt at a Solution Limitation-air...

I'm trying to work out the differential equation for simple harmonic motion without damping, x''+\frac{k}{m}x = 0 I can solve it to x = c_1cos(\sqrt{\frac{k}{m}}) + c_2sin(\sqrt{\frac{k}{m}}) But the generalized solution is x = Acos(\omega*t + \delta) where A = \sqrt{c_1^2 + c_2^2}...

So, simple harmonic motion without damping is described generally by x(t) = Acos(\omega*t +\delta) Which is derived from the differential equation x''+\frac{k}{m}x = 0 We know that A = \sqrt{c_1^2+c_2^2} and tan\delta = \frac{c_1}{c_2} With the differential equation, dealing...

Homework Statement Does this converge or diverge? Ʃ1/(1+2+3+4+5...+n), as n---> infinity?The Attempt at a Solution I rewrote this into Ʃ(Ʃ1/n) (is it correct?). I figured that since Ʃ(1/n) diverges, then the sum of each partial sum most (obviously) also diverge. However, it appears I'm...

What is a space/spatial harmonic? Hi I am doing a project on folded waveguides and I am reading some IEEE papers for literature review. I always come across this term "space harmonic" and fail to understand what it is. I have checked online but don't get it. Even posted in the Electrical...

HI! I was wandering if there is a proof that the harmonic sum \sum\frac{1}{k} has no closed form. Something like the proof that an equation with degree more than 4 has no solution in terms of radicals.

Hi, why does the harmonic plane wave have the form below: V(r,t)= acos[\omega (t-\frac{r\cdot s}{v})+\delta ] (r is the position vector, s is the vector that points to the direction the wave is propagating, v is the wave propagation velocity and delta is the phase constant).

Homework Statement Let Sn = 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}...+\frac{1}{n}. Show that |S2n-Sn|\geq \frac{1}{2} Homework Equations The Attempt at a Solution So I'm going to try and use induction Base case let n=1 |S2n-Sn| = \frac{1}{2} So true for base case...

Hi,I am Vikas Joshi and I'm studying last year Electronics Engineering. I am doing project on Harmonics Monitoring using Micro-controllers. I have some doubts about it.They are as follows: 1.How to detect Harmonics from Single Phase supply.What kind of circuits I should use to detect specific...

When people talk about harmonic oscillators it seems to me that they always assume either that the relationship of force and displacement is linear, or that it behaves in some sinusoidal fashion. Do you always have to assume one to be able to arrive at the other? Or is there something I'm...

Homework Statement particle experiencing SHM with frequency f= 10 hz find the displacement x at any time t for the following initial conditions. @ t=0 x=0.25m v=0.1 m/sHomework Equations x=Asin(ωt+∅) v=Aωcos(ωt+∅)The Attempt at a Solution So with frequency I find ω which then is subbed into...

Find under what conditions the transformation from (x,p) to (Q,P) is canonical when the transformation equations are: Q = ap/x , P=bx2 And apply the transformation to the harmonic oscillator. I did the first part and found a = -1/2b I am unsure about the next part tho: We have the...

Homework Statement A 3D harmonic oscillator has the following potential: V(x,y,z) = \frac{1}{2}m( \varpi_{x}^2x^2 + \varpi_{y}^2y^2 + \varpi_{z}^2z^2) Find the energy eigenstates and energy eigenvalues for this system. The Attempt at a Solution I found the energy eigenvalue to...

I was reading a book on wave and found that when they derive the equation of shm from the equation force varies with negetive displacement , they had taken a propotionality constant to make the force and displacement equal and they had taken frequency of the shm as the constant . So my question...

Homework Statement Find the energy eigenvalue. Homework Equations H = (p^2)/2m + 1/2m(w^2)(x^2) + λ(x^2) Hψ=Eψ The Attempt at a Solution So this is what I got so far: ((-h/2m)(∂^2/∂x^2)+(m(w^2)/2 - λ)(x^2))ψ=Eψ I'm not sure if I should solve this using a differential...

The function for simple harmonic oscillation is: Acos(ωT)+\phi Why is there an angle phi added to the function acos(ωT)?

Homework Statement (See attachment) Homework Equations x = \sqrt{\frac{\hbar}{2m \omega}} ( a + a^{\dagger} ) x = i \sqrt{\frac{\hbar m \omega}{2}} ( a^{\dagger} - a ) The Attempt at a Solution In part a) I was able to construct a separable Hamiltonian for the harmonic...

Homework Statement Consider an underdamped harmonic oscillator (Q > 1/2) with a sinusoidal driving force Focos(ωdt). (a) (5 pts) By using differential calculus find ωd that maximizes the displacement amplitude. (b) (7 pts) By using differential calculus find ωd that maximizes the velocity...

Consider a light flexible rod placed on a horizontle table with part of the rod (length say "x") hanging freely (ie without support of the table) see attachment for clarity A mass is also hung from the rod t one end. Are there any equations that relate the Period T of the end of the rod to...

Ground State Wave Equation: ψ0=(a/∏)(1/4)e(-ax2/2) Prove the Heisenberg Uncertainty principle ≥h(bar)/2 by way of expectation values. First I found <x>=0 because it was an odd function then I found <Px>=0 because it was an odd function Then <x2>=∫(a/∏)(1/2)x2e(-ax2)/2dx=1/2a by way of...

So my friend and I were going through problems and this came up... Consider 3 straight, infinitely long, equally spaced wires (with zero radius, separated each by a distance d), each carrying a current I in the same direction. blah blah blah... part c) asks us... If the middle...

I believe this is pretty standard. Given a mass m on a spring with spring constant k, a solution to the second order differential equation of motion m\ddot{x} = -kx, is x = cos ωot, and ωo = \sqrt{k/m}. If that same oscillator is driven with a force F(t) = Fo cos ωt the equation of motion...

Homework Statement A simple harmonic oscillator has an amplitude of 0.1 m. At what displacement will its kinetic and potential energies be equal? Homework Equations The Attempt at a Solution I'm trying to figure out how to solve this problem but I'm totally stuck and even don't...