Harmonic Definition and 1000 Threads

I know that simple harmonic motion is a type of periodic motion where the restorative force is directly proportional to the displacement so that the time evolution is sinusoidal but is there such a thing as just harmonic motion? 0r is harmonic motion just short for simple harmonic motion?

Homework Statement The problem wants me to calculate (Δx)^2 and (Δp)^2 to find the uncertainty principle. Delta x is the variance and the problem gives the formula as.. Δx= <n|x^{2}|n>-<n|x|n>^{2}Homework Equations x=\sqrt{\frac{\hbar}{2m \omega}}(A^{-}+A^{+}) Where A+ and A- are the raising...

This is a problem I've been trying to solve for quite some time now. Any help would be appreciated. Homework Statement When a person with the mass of 105kg sits in a car, the body of the car descends by 2,5cm in total. In the car there are four shock absorbers filled with oil and a spring...

Homework Statement A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest: a.) find the force between the bottom of the box and the block as a function of time...

Homework Statement Show ln(az) where a is a real number and z = x + iy is harmonic everywhere except z = 0. Homework Equations z = x + iy = rcos(θ) + irsin(θ) = re^iθ z = u(x,y) + iv(x,y) Cauchy Riemann test for analyticity: ∂u/∂x = ∂v/∂y ∂u/∂y = -∂v/∂x The Attempt at a...

Homework Statement The displacement amplitude of a lightly damped oscillator with m=0.250kg and k=6400N/m is observed to decrease by 15% in exactly five minutes a) Calculate the fraction (in%0 of the initial mechanical energy of the oscillator that has been converted to other forms of energy...

Homework Statement A block rides on a piston that is moving vertically with simple harmonic motion. (a) If the SHM has period 2.65 s, at what amplitude of motion will the block and piston separate? Homework Equations x(t)=xmcos(ωt + ∅) a(t)=-w2xmcos(ωt + ∅) Where xm is the amplitude...

A bucket of mass 2.0 kg containing 10 kg of water is hanged on a vertical ideal spring with constant 125 N/m, oscillating up and down with an amplitude equal to 3.0 cm. Suddenly arises a leaky in the bottom of the bucket so that the water flows at constant rate of 2.0 grams/s. When the bucket...

Homework Statement A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest: a.) find the force between the bottom of the box and the block as a function of time...

Homework Statement Derive the expression v = lnfn where ln is the shortest distance between nodes for the nth harmonic. Homework Equations v = wave speed ln = shortest distance between nodes for the nthharmonic fn = frequency of the nth harmonic The Attempt at a Solution Is it...

Homework Statement Two blocks mass m1 and m2 (m1 greater than m2) are joined by a spring (which can extend and compress) and both rest on a horizontal frictionless table. the blocks are pulled apart, held at rest and then released. describe and explain as fully as you can the sibsequent...

Hello, I am trying to derive the harmonic content of a signal passing through a transistor's transfer function. After a Taylor expansion in Mathematica 7, I have the expanded equation and the next step is to reduce everything to first order Sine/Cosine functions. In Mathematica, if I have a...

Homework Statement A harmonic oscillator has angular frequency ω and amplitude A. What is the magnitude of the displacement when the elastic potential energy is equal to the kinetic energy? (Assume that U = 0 at equilibrium.) Express your answer in terms of the variables ω and A...

×Homework Statement A lift cable has mass per unit length 4kg/m. The lift has mass of 920kg (assume that the tension in the cable is provided solely by the weight it supports). When the lift stops at the 3rd floor, the distance from the top of the lift to the top of the cable is 4.6m. Assuming...

Homework Statement A block with mass m =7.1 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.5 m/s. The block oscillates on the spring without...

Homework Statement A metal sphere of mass 0.20kg is hung from a helical spring whose top end is clamped. the sphere is displaced by 0.030m below its equilibrium position, and then released. 20 cycles of oscillation, of amplitude 0.030m, occur in a time of 12.0s. calculate; (I) the spring...

Challenge Problem: A variable line $L$ passing through the point $B(2,5)$ intersects the lines $2x^2-5xy+2y^2=0$ at $P$ and $Q$. Find the locus of the point $R$ on $L$ such that distances $BP$, $BR$ and $BQ$ are in harmonic progression.

I have to solve the following D.E. which describes how the amplitude of oscillation r, changes with time. r=f(t) \frac{dr^{2}cos^{2}t}{dt}=rsint How do I find r?

hello, new here and confused about Newton second Law. given: vertical mass damper system, position of the mass: x(t)=sin(t) velocity is: v(t)=cos(t) acceleration is: a(t)=-sin(t) function x(t): above x-axis describes position of the mass below the vertical equilibrium point, which (below) is...

I need to find the value σ for which: ψ0(x) = (2πσ)-1/4 exp(-x2/4σ) is a solution for the Schrodinger equation I know the equation for the QHO is: Eψ = (P2/2m)ψ + 1/2*mw2x2ψ I've tried normalizing the wavefunction but I end up with a σ/σ term :( Any help would be greatly...

The question is: A 56.0 kg bungy-jumper hangs suspended from her bungy-cord, at rest. She is displaced from this position by 15.0 m downward, and then released. She bounces up and down, with a period of 5.800 s. Assume the woman undergoes simple harmonic motion, described by y(t) = X cos(2...

Homework Statement The motion of a particle is given by: x = (6.0m) cos(0.586t + 0.72) a) Find the amplitude b) Find the Period c) Find the first time for t>0 when v=0 d) Find the maximum acceleration e) Fine the phase at time t=1.38s Homework Equations x = A cos ωt T =...

Homework Statement A particle moving in simple harmonic motion with a period T = 1.5 s passes through the equilibrium point at time t0 = 0 with a velocity of 1.00 m/s to the right. A time t later, the particle is observed to move to the left with a velocity of 0.50 m/s. (Note the change in...

Homework Statement A spring is hung vertically from a support. A mass of 4.5 kg is hung from the lower end of the spring and is slowly lowered a distance of 22.0 cm until equilibrium is reached. This mass is then lowered to a point 15.0 cm below the equilibrium point and is then released...

Homework Statement A 250 gram mass is connected to a spring and executes simple harmonic motion. The period of motion is 0.5 seconds and the total mechanical energy is 0.50J. What is the amplitude of motion? Homework Equations ΔU = 1/2kx2 The Attempt at a Solution I get 1/2kx2 =...

Hi Here is my code to get the sum of harmonic series. Harmonic series is \sum_{i=1}^{\infty}\; \frac{1}{i} here is the code program harmonic implicit none integer :: i,n real :: sum=0.0 write(*,*)'How many terms you want to sum ?' read(*,*) n do i= 1 ,n...

I've been set this question by my tutor and I'm having difficulty doing it. A mass of 2 kg is hung from the lower end of a vertical spring and extends it by 40 cm. The mass is now pulled down a further 20 cm and is then released from rest so that it oscillates about the equilibrium position...

Over which interval do the wave functions of a harmonic oscillator form a complete and orthogonal system? Is it (-inf,+inf)? The case with particle in a box is rather clear(system is complete and orthogonal only for the interval of the well), however the harmonic oscillator is a bit less intuitive.

Hello. I was trying to find out the propagator for the inverted SHO (something like tachyon oscilltor) and turns out that it remains unitary only for very short times. Which didnt make much sense to me. I tried looking at the usual SHO propagator, and that too seems to be not Unitary! ( I...

here is a link to the pdf file with my question and answershttp://dl.dropbox.com/u/2399196/harmonic%20osc.pdf i'm not sure where to start, because i don't want to assume anything that i haven't been given. i'm stuck on part (iv) where i have to derive explicit expressions for 2 wave functions...

I've heard before that it's because when you expand around a minimum point in the potential energy you get a quadratic function, but I can't recall where I read this. Can anyone point me in the right direction, or give their own explanation? I only ask because I just solved a problem in my...

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...

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 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 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...