Harmonic Definition and 1000 Threads

Hello everybody. Here is a ( I hope) simple question that can't let me sleep. The question is : At the course of physics one of the greatest profesors. Dr. Lewin drew a simple equation that 10Tm(2)= √m(2)/M(1) times 10Tm(1) . It was a harmonic oscilator composed by two object placed on a...

Homework Statement Given a positive subharmonic function u , defined on R^2 , how can I prove that u[ /itex] must be constant? Homework Equations \Delta u \leq 0 is the definition of subharmonic function ! The Attempt at a Solution I've tried solving this by using a new...

Hi I would like to know if I have a system of coupled harmonic oscillators whether the standard position operator for an uncoupled oscillator is valid, i.e. x_i = \frac{1}{\sqrt{2}} (a_i+a_i^\dagger)? where i labels the ions. To give some context I am looking at a problem involving a...

Just have a few questions regarding the method of solving the damped-driven harmonic oscillator. Once we have rewritten the differential equation in terms of z and it's derivatives, we try a solution z(t) = Ce^{i \omega t}. When we sub in z and it's derivatives we then rewrite the complex...

Homework Statement Let u be a continuous real-valued function in the closure of the unit disk \mathbb{D} that is harmonic in \mathbb{D}. Assume that the boundary values of u are given by u(e^{it}) = 5- 4 \cos t. Furthermore, let v be a harmonic conjugate of u in \mathbb{D}...

Homework Statement If the phase angle for a block-spring system in SHM is π/5 rad and the block's position is given x = xm cos(ωt + phi), what is the ratio of the kinetic energy to the potential energy at time t = 0? Homework Equations PE = (1/2)*k*[(max amplitude)^2]*cos^2(ωt + phi)...

Hi all, apologies if this has been answered elsewhere - I was unable to find an answer using the search function. Homework Statement "Expressed in terms of wavenumber and angular frequency, the equation for a traveling harmonic wave is: y = Asin(kx-ωt). Express this function in terms of (a)...

Hi there, SalsaOnMyTaco here again. Homework Statement A 44 gram mass is attached to a massless spring and allowed to oscillate around an equilibrium according to: y(t) = 1.2*sin( 3.1415*t ) where y is measured in meters and t in seconds -What is the spring constant in N/m ? HELP...

Homework Statement I have trouble determining the system of forces in systems with strings like the following: Homework Equations The Attempt at a Solution My guess is it is: x1=L/3 x2=2L/3 mass 1: -kx1+k(x2-x1)=m1a1 mass 2: -k(x2-x1)+kx1=m2a2 I'm not sure...

Homework Statement A physical system is designed having the following equation of motion md2x/dt2 + c(dx/dt) - kx = 0. (a) From the corresponding subsidiary equation, find the solution to this equation of motion. (HINT: use the solution of the damped harmonic oscillator as a guide)...

(a) A box of mass m, attached to a spring, oscillates in simple harmonic motion on a frictionless surface as indicated in the figure below. Each time the box reaches the point of maximum displacement a child allows some sand to fall vertically into the box. This will gradually increase the mass...

the problem is attached as an image. im having troubles with the question. I'm assuming this is an induction question? i can prove it for the basis step n=0. but I am having trouble as to what i have to do for n+1 (inductive step). any help or hints would be great!thanks

Homework Statement Find a particular solution to the differential equation using undetermined coefficients. x^{''}+5x^{'}+4x=2sin2t x(0)=1 x'(0)=0 I know that the equation is underdamped because c<W_{0}, and that W_{0}=2. I know that the particular solution is...

Homework Statement A mass is oscillating on a spring with simple harmonic motion. Its amplitude is 0.80m and its maximum speed is 1.5m/s, at the point of equilibrium. What is the speed of the mass at 0.60m? Is there enough information to answer this question? The answer given is 0.75m/s...

A body moving with simple harmonic motion has an amplitude of 1 meter and the time for one complete oscillation is 2 seconds . Determine the velocity and acceleration of the body after 0.4 second from the mean position ? this is the answer : Vx = w root(r^2-x^2) ax=w^2.X w= 2Pi/t =...

Homework Statement Natural length is "l" and when a "m" mass is hanged on the P edge, it dragged by another "L" length. Point "O" is "4L" far from the floor. 1. Find \lambda 2. The mass will be hold at point "O" and released with the starting velocity √(gL). Find the velocity of the mass after...

Hi guys! I'd really like help with this as I'm stuck. Homework Statement Investigate the mathmatical relationship between period of a spring and mass. Finding the spring constant (k) from measuring periods with a spring and different hanging masses. Homework Equations T = 2pi...

Homework Statement A particle moves with SHM in a straight line. In the first second after starting from rest,it travels a distance of 1m in a constant direction. In the next second, it travels a distance of 2m in the same direction. Find its maximum acceleration Homework Equations...

Homework Statement http://img534.imageshack.us/img534/6503/questiono.jpg Homework Equations The Attempt at a Solution (a) I'm not sure how to approach this part. I appreciate any help to get me started. (b) I know that the period of oscillation is given by T'=\frac{2 \pi}{\omega '} I...

Homework Statement trying to write a program in C++ to calculate the solution of a damped harmonic oscillator and compare with the exact analytic solution. i am using the classic 4th order Runge-Kutta, which I'm fairly sure is programmed right. Homework Equations m\ddot{x} + c\dot{x}...

Homework Statement A damped harmonic oscillator loses 6.0% of it's mechanical energy per cycle. (a) By what percentage does it's frequency differ from the natural frequency f_{0} = (\frac{1}{2\pi})\sqrt{\frac{k}{m}}? (b) After how many periods will the amplitude have decreased to...

Homework Statement Consider a quantum mechanical particle moving in a potential V(x) = 1/2mω2x2. When this particle is in the state of lowest energy, A: it has zero energy B: is located at x = 0 C: has a vanishing wavefunction D: none of the above Homework Equations The...

Homework Statement A car with mass 1220kg including the driver travels over a bridge with expansion gaps spaced 5.5m apart. At a speed of 12.0m/s, the car bounces up and down with exceptionally large amplitude. Two more 80kg passengers now get in the car. a) What speed will result in maximum...

Homework Statement A high pass filter tuned for a corner freq. of 40 000 rad/sek and with a damping coeffisient of 1/sqrt(2) is being subjected to a square wave voltage with amplitide of 1 volt and 8000 rad/sek. What is the amplitude of the fifth harmonic on the output side of the filter...

Homework Statement An object of mass m is suspended from a vertical spring of force constant 1800 N/m. When the object is pulled down 2.50 cm from equilibrium and released from rest, the object oscillates at 5.500 Hz. a) Find m, b) Find the amount the spring is stretched from its unstressed...

Homework Statement When a 0.870kg mass oscillates on an ideal spring, the frequency is 1.33Hz. a) What will the frequency be if 0.290kg are added to the original mass? Try to solve this problem without finding the force constant of the spring. b) What will the frequency be if 0.290kg are...

Homework Statement I need to transform the Hamiltonian of a coupled Harmonic Oscillator into the sum of two decoupled Hamiltonians (non-interacting oscillators). Homework Equations H = H1 + H2 + qxy, where H1=0.5*m*omega^2*x^2+0.5m^-1P_x^2 and H2=0.5*m*omega^2*y^2+0.5m^-1P_y^2, and q is...

Homework Statement Use a series expansion ψ=A0x0+A1x1+A2x2+... to determine the three lowest-order wave functions for a harmonic oscillator with spring constant k and mass m, and show that the engergies are the expected values. Homework Equations Series expansion given above Time...

Homework Statement Let S_n = 1 + (1/2) + (1/3) + (1/4) + ... + (1/n) a) What value of n is required such that S_n > 100? b) Show how one can form a stack of identical blocks (one per row), each 1 ft long, so as to form a "wing" (I don't know what the correct word in English is, but I...

Homework Statement Clock activates escapement every time it passes through the vertical. Escapment under tension from a hanging weight that gives an impulse distance l from the pivot. Energy transferred by this compensates for the energy dissipation due to friction so the amplitude is...

good afternoon I am a graduate student in Jordan and i am working on my graduation project about harmonic studies in our university hospital and I've got data from power analyzer -all harmonics voltages and currents until 25th harmonic (sampling every 1 min). -all rms data currents...

Can someone explain to me how a low pass harmonic filter works in laymens terms? I would really appreciate it?

Hi, I am currently confused about something I've run across in the literature. Given that \nabla^2\phi = \phi_{xx}+\phi_{zz} = 0 for z\in (-\infty, 0] and \phi_z = \frac{\partial}{\partial x} |A|^2 at z=0. for A= a(x)e^{i \theta(x)} . The author claims that...

I had my physics midterm today and I totally blanked out. I want to know how to solve it for next time. So In the picture, there are two springs connected to the mass on a platform. a) if the platform is at rest, find the angular frequency the expression for angular frequency is...

Hello everyone, i'm looking for anypaper or such kind of thing that explain the resolution of the harmonic oscillator in the Dirac Theory. I have worked with the exact spin symmetry. I feel like a fish out the water and I'm sure that there are lot of bibliography about this area, but i...

Homework Statement A 200-g object is oscillating in simple harmonic monition with an amplitude of 2 cm and a period of 0.4 seconds. Find the velocity when its displacement from the equilibrium position is 0.5 cm. Homework Equations Restoring Force = -(constant force)(displacement)...

Homework Statement An elastic string is attached to A on a horizontal plane and a mass is attached to the other side of the rope.Then the rope is pulled to C and release.It engage in SHM from C to B and D to E and so on natural length = l extension = a max end points = E & C...

I have fashioned permanent magnet alternators with air cores and with iron cores. The air core units generate a sine wave (or something close to it), but the iron core units have third order harmonic distortion, (see waveform). Why is this?

Homework Statement Given an initial (t=-∞) Fock state , \left|n\right\rangle, and a function f(t), where f(±∞)=0, show that for a Harmonic Oscillator perturbed by f(t)\hat{x} the difference \left\langle H(+∞) \right\rangle - \left\langle H(-∞) \right\rangle is always positive.Homework Equations...

Homework Statement A 1.00-kg glider attached to a spring with a force constant 49.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is released from rest at x = -3.50 cm (that is, the spring is compressed by 3.50 cm). Find the position, velocity, and...

Homework Statement An object is undergoing simple harmonic motion with period 1.190 and amplitude 0.640 At t=0 the object is at x=0 . How far is the object from the equilibrium position at time 0.475 ? Homework Equations The Attempt at a Solution x=Acos(ωt+∅) x=...

Homework Statement An object is undergoing simple harmonic motion with frequency = 3.2 Hz and amplitude = 0.12 m. At = 0 the object is at = 0. How long does it take the object to go from = 0 to = 7.2×10−2 m? Homework Equations The Attempt at a Solution s(t)=Asin(ωt)...

Homework Statement Show that: \frac{1}{2\pi}\int_0^{2\pi}log|re^{i\theta} - z_0|d\theta = \left\{\begin{matrix} log|z_0| & if & |z_0| < r \\ log|r| & if & |z_0| > r \end{matrix}\right. Homework Equations The function log|z| is harmonic in the slit plane since it is the real part of log(z)...

Homework Statement A block is attached to a horizontal spring with k = 75 N/m undergoes SHM with an amplitude of 0.15m. If the speed of the block is 1.7 m/s when the displacement is 0.12m from equilibrium, what is the mass of the block?Homework Equations E = E' E_{k} = \frac{1}{2}mv^{2} E_{s} =...

An object of mass m is supended from a vertical spring of force constant 1269 N/m. When the object is pulled down 0.068 m from equilibrium and released from rest, the object oscillates at 10 Hz. The mass of the object is ____ kg. τ= 2∏*sqrt(M/K) M = mass K = spring constant 1/f = τ...

Homework Statement A pipe has a length of 1 m. Determine the frequency of the first harmonic if the pipe is open at each end. The velocity of sound in air is 343 m/s. Answer in units of Hz Homework Equations f = v/2L The Attempt at a Solution I just did another problem like...

Homework Statement Consider a steel spring with the property that it extends by 10cm (0.1m) in equilibrium when you attach the upper end of the spring to a fixed support and hang a weight of 100g (0.1kg) at the springs lower end. 1) Use the equation for the harmonic oscillator to determine...

Homework Statement A 4kg mass remains at rest on a friction free surface due to equal and opposite pulls of two springs. Spring 1 is stretched 4 meters. The k in spring 1 equals 40 N/m and the k in spring 2 equals 60 N/m. This is what the the picture looks like in words. From left to the...

Homework Statement A mass m is attached to a spring of stiffness k. The spring is attached to the ceiling and the mass hangs freely from the spring under the force of gravity. (a) Derive the equation of motion for this system. (b) Find an expression for the equilibrium position of the...

Homework Statement Evaluate the matrix elements x_{nn'} = \left<n\left|x\right|n'\right> and p_{nn'} = \left<n\left|p\right|n'\right> and map the energy eigenstates \left|n\right> to Cartesian unit vectors. Homework Equations x = \sqrt{\frac{\hbar}{2m...