Harmonic Definition and 1000 Threads

Homework Statement Show that the following is an eigenfunction of \hat{H}_{QHO} and hence find the corresponding eigenvalue: u(q)=A (1-2q^2) e^\frac{-q^2} {2} Homework Equations Hamiltonian for 1D QHO of mass m \hat{H}_{QHO} = \frac{\hat{p}^2}{2m} + \frac{1}{2} m \omega^2 x^2...

This is not really a homework problem but rather a question about an equation for displacement in damped harmonic oscillations that I've come across during revision for midterms. In my notes and in various textbooks the equation is given as x=C\mathrm{exp}(-\frac{b}{2m}t)\cdot\mathrm{exp}(\pm...

Homework Statement In my notes it is stated that an integrator adds a phase lag of -Pi/2 and thus can cause instability. I want to understand what this really means and am deviating from the notes somewhat so do not know if I am barking up the wrong tree. Homework Equations Given a...

Homework Statement Particle of mass m undergoes simple harmonic motion along the x axis Normalised eigenfunctions of the particle correspond to the energy levels E_n = (n+ 1/2)\hbar\omega\ \ \ \ (n=0,1,2,3...) For the two lowest energy levels the eigenfunctions expressed in natural...

Period does not depend on amplitude. Correct? I deduced this from the equations for simple harmonic motion: ω=2πf ω=√(k/m)

Their equations are identical. Is there any difference between the two?

x(t)=Acos(ωt+ϕ)\\v(t)=-ωAsin(ωt+ϕ) I think my physics professor said in one of the lectures that: after setting up your position function by finding amplitude, angular speed, and solving for ϕ by setting t=0 and using the x(0) value given in the question, you need to to set t=0 in the velocity...

Homework Statement A mass is attached to a spring with a force constant of 32N/m. The spring and the mass are set into simple harmonic motion on a frictionless, horizontal surface. The period of vibration of this mass is 0.4 seconds. a) Calculate the object's mass b) Calculate...

Homework Statement Ok, basically I need to show that Ʃ 1/n (between 1 and n) (which is harmonic number) is θ (big theta) of ln(n), which means that is it bounded below and above by this function(upper and lower bound). But I don't quite understand how to prove it.Homework Equations I know...

Homework Statement Consider as an unperturbed system H0 a simple harmonic oscillator with mass m, spring constant k and natural frequency w = sqrt(k/m), and a perturbation H1 = k′x = k′sqrt(hbar/2m)(a+ + a−) Determine the exact ground state energy and wave function of the perturbed system...

Homework Statement Consider a system of N localized particles moving under the influence of a quantum, 1D, harmonic oscillator potential of frequency ω. The energy of the system is given by E=(1/2)N\hbarω + M\hbarω where M is the total number of quanta in the system. compute the total...

Trust me this is not homework... My last two questions were removed cause they looked like homework... I understand its the forum policy... From now on I will post the 'seemingly homework' on the homework sections... Suppose,there's a rod of mass m1 hanging from a point... And a mass m2 is...

Hey, My question is on determing the expectation value of position of the Harmonic Oscillator using raising and lowering operators, the question is part d) below: I have determined the position operator to be: \hat{x}=\sqrt{\frac{\hbar}{2m\omega}}(a+a^{\dagger}) and so the...

Homework Statement Prove that that the power given by \bar{P} = \frac{1}{2} \gamma m \omega_r^2 A_{(\omega)}^2 is at a maximum for \omega_r = \omega_0 Only variable is \omega_r \omega_r is the resonant frequency of the external force while \omega_0 is the eigen frequency of the...

Homework Statement The position of a mass that is oscillating on a Slinky (which acts as a simple harmonic oscillator) is given by 18.5 cm cos[ 18.0 s-1t]. What is the speed of the mass when t = 0.360 s? Homework Equations x(t)=Acos(ωt+θ) v(t)=-Aωsin(ωt+θ) The Attempt at a Solution...

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!

Homework Statement The 3-dimensional harmonic oscillator potential holds N identical non-reacting spin 1/2 particles a)How many particles are needed to fill the low lying states through E=(3+3/2)\bar{h}ω b)What is the total energy of the system c)what is the fermi energyHomework Equations...

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.

Homework Statement My textbook (Churchill) is asking me to prove that the contours $$u(x,y) = c_1$$ and $$v(x, y) = c_2$$ where $$u$$ and $$v$$ are the real and imaginary components of an analytic function $$f(z)$$ are orthogonal at any point by noting that $$u_x + u_y \frac{dy}{dx} = 0 $$ and...

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 The hyperbolic coordinate sysem onthe first quadrant in R^2 is defined by the change of variables K(u,v)=(x(u,v),y(u,v))=(ve^u,ve^(-u)) u is in R,and v>0, find all harmonic functions on the first quadrant in R^2 which are constant on all rectangular hyperbolas xy=c , c is a...

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...