Harmonic Definition and 1000 Threads

Homework Statement Homework Equations Where do the terms 1/4 come from? Are they ambiguous? The Attempt at a Solution Trying to understand the text[/B]

Homework Statement Express $$4sin\theta-3cos\theta$$ in the form $$rsin(\theta-\alpha)$$ Hence find the maximum and minimum values of $$\frac{7}{4sin\theta-3cos\theta+2}$$ State the greatest and least values. Homework EquationsThe Attempt at a Solution Okay so putting it in the...

Homework Statement Using the equations that are defined in the 'relevant equations' box, show that $$\langle n' | X | n \rangle = \left ( \frac{\hbar}{2m \omega} \right )^{1/2} [ \delta_{n', n+1} (n+1)^{1/2} + \delta_{n',n-1}n^{1/2}]$$ Homework Equations $$\psi_n(x) = \left ( \frac{m...

A 12kg mass undergoes simple harmonic motion with an amplitude of 10cm. If the force constant for the spring is 320N/m: a) Calculate the total energy of the mass spring system. Et=½kA^2 =½(320N/m)(0.1m)^2 =1.6 Jb) Calculate the maximum speed of the mass. Et=½mv^2 + ½kx^2 1.6 J = ½(12kg)v^2...

Homework Statement I'm using a couple different textbooks on waves, and it seems they've possibly contradicted one another. I think the problem may be that one deduced the equation for displacement in a transverse harmonic wave y(x,t) through the equation for displacement at t=0 [y(x,0)] and...

Hi, What is the physical meaning of zero probability of finding a particle in the square of the Quantum SHO wave function? the particle is supposed to oscillate about the equilibrium position, how would it go from an end point to the other end point without passing by certain points? Could the...

Hey, I'm stuck halfway through the solution it seems. I could use some tips on how to continue. 1. Homework Statement I have to determine a linear combination of the states |0\rangle, |1\rangle, of a one dimensional harmonic oscillator, so that the expectation value \langle x \rangle is a...

Homework Statement Two positive charges +Q are affixed rigidly to the x-axis, one at x = +d and the other at x = -d. A third charge +q of mass m, which is constrained to move only along the x-axis, is displaced from the origin by a small distance s << d and then released from rest. (a) Show...

I lightly placed my finger a quarter of the length down the E-string of a violin and drew the bow, forcing the third harmonic. I used an oscilloscope app to look at the waveform. I got this unusually regular pure pattern...

V=Vo √1-(x^2/a^2) X is the distance of the spring's stretch, but how would you rearrange the equation if you are looking for Amplitude? They both use the same units (meters) as far as I am concerned. Help would be appreciated, thanks; I am still a beginner with Physics.

Hi there, I am reading something about the bose-einstein condensate, in this material http://www.physics.ox.ac.uk/qubit/fetch.asp?url=groupwebsite/papers/paper103.pdf , it states something called harmonic trap. I read other introduction materials on bose-einstein condensate, it said that to...

Homework Statement Can I get help in part (b) of this question ? Homework Equations KE=1/2 m v2 v= (2π f )√(A2 - x2) The Attempt at a Solution I substituted the second equation into first one, so i got KE= 1/2 m (2π f )2 (A2 - x2) but then couldn't complete

Homework Statement What is the normalized ground state energy for the 3-D Harmonic Oscillator Homework Equations V(r) = 1/2m(w^2)(r^2) The Attempt at a Solution I started with the wave fn in spherical coordinates, and have tried using sep of variables, but keep getting stuck when trying to...

Homework Statement An instrument is producing a tone, such as a D4. If I know the frequency of the tone, the length of the instrument but nothing else, how can I find the harmonic at which the tone is produced? The instrument is an open tube. Homework Equations v=wavelength*frequency[/B]...

I'm asked to Calculate the frequency of oscillation of a simple pendulum of length 80cm. As its a pendulum I used To calculate the time. To which I got 4/7π I then used f=1/period and converted 80cm to 0.8m and got a frequency of 0.577Hz, is this correct ?

This is a really basic calc/physics question.If acceleration is defined as Acc= Asin(w*t), and I integrate this to get velocity, I get Vel=(-A/w)*cos(w*t)+C. If the velocity at t=0 is 0, then C=A/w. If I then integrate the velocity to get the displacement, I get...

Homework Statement [FONT=Arial]A L = 1.48 m long metal rod is pivoted from a point one third of the way along its length. The rod has a mass of 0.208 kg. What period will the rod oscillate with when released from a small angle? Homework Equations T = 2 \pi \sqrt{\frac{L}{g}} The Attempt...

I was wondering whether it's possible to write a code in C++ that would be able to solve the Harmonic Oscillator: \ddot{x} + \gamma x = F_{external}(t,x) With different F function inputs... I thought about creating a function with if clauses, so for different inputs by the user, the force F...

My question concerns a really simple differential equation for the zeroth wavefunction of a harmonic oscillator. I have pretty much got it but my solution just differs by a constant,so I thought why think when one can ask other people :). Here is the equation: Where the x star represent a...

1. The balance spring of a watch is a hoop 1.2 cm in diameter, with a mass of 0.65 g. If the watch is running 45 seconds per day too fast, by what percentage should the rotational inertia of the hoop be changed? 2. Homework Equations : I = mR^2 Ia = -k(theta) x(t) = Xm Cos(wt + @) (just using @...

A 350-g mass is attached to a spring whose spring constant is 64 N/m. Its maximum acceleration is 5.3 m/s2. What is its maximum speed? So, i had a go at the question which basically required the knowledge that maximum acceleration occurs when displacement is maximum and maximum velocity occurs...

Given the half harmonic potential: \begin{equation}V=\begin{cases}1/2\omega^2mx^2 & x > 0\\\infty & x < 0\end{cases}\end{equation}What will be the Hamiltonian of the half oscillator?I understand that for x>0 the Hamiltonian will be...

I was wondering why the average kinetic energy is calculated in this manner. They are dividing the kinetic energy function by the period (noted here as To) and integrating it with limits from 0→To. Why? (This is a tiny portion of a larger textbook example, not an actual assignment.) Sorry for...

Homework Statement The transition amplitude for the harmonic oscillator may be written as ##\langle x_2, t_2 | x_1, t_1 \rangle = N_{\omega}(T) \exp(i/\hbar S_{cl})##, where ##T=t_2-t_1## and ##S_{cl}## is the classical action. Let the wave function at ##t=0## be ##\psi(x,o) =...

Homework Statement A particle of mass m in the one-dimensional harmonic oscillator is in a state for which a measurement of the energy yields the values ##\hbar\omega/2## or ##3\hbar\omega/2## each with a probability of one-hald. The average value of the momentum ##\langle p_x\rangle## at...

Homework Statement An 8.0 lb block is suspended from a spring with a force constant of 3.0 lb/ in. A bullet weighing 0.10 lb is fired into the block from below with a speed of 500 ft/sec and comes to rest in the block. a) Find the amplitude of the resulting simple harmonic motions b) What...

Homework Statement How is ##\frac{v}{v_M} = \frac{\sqrt{A^2 - x^2 }}{A}## derived? Homework Equations n/a The Attempt at a Solution I don't see a right angle in the picture anywhere, so I don't see how pythagorean's theorem is valid.

Homework Statement My textbook states that for simple harmonic motion, the sinusoidal graph of the x (displacement) as a function of time can be created using the "Equation of motion". Homework Equations The equation of motion ##A \cos (\omega t + \phi)## The Attempt at a Solution I know...

Hello, I was asked by my professor today to graph the motion, as well as the energies, of a spring that undergoes driven and/or damped oscillation; however, I was unable to because I do not have a very good idea of how they work. Can someone explain to me, qualitatively, what it means to have a...

This is not a homework question per se, but rather something I have come across during a homework project. Using Audacity, I recorded a few different instruments playing the same notes (investigating timbre). I noticed that (using a steel string acoustic guitar) the first harmonic at 131 Hz...

For the harmonic oscillator in 1-D we get the 2nd time derivative of the x Heisenberg operator = -ω2 x. When that is integrated it gives xH (t) = Acos(ω t) +Bsin (ω t) where A and B are time independent operators. My question is why are the constants A and B incorporated into the terms as a...

Hello there! I have a simple question; Why simple harmonic motion is called simple harmonic motion? What's the origin of this name? I could not find the answer despite browsing so many websites on the internet. Could anybody tell me the answer? Thanks in advance.

I'm trying to figure out how to derive the equations for Energy from the differential equation corresponding to the (simple and damped) harmonic oscillator. Please note that I don't want to start with the expressions for kinetic and potential energy, I want to derive them. The references that I...

Hello, I'm was going through the simple harmonic oscillator, just as a recap, and I stumbled upon something which is causing me wonder. I'm solving the SHO with a shifted origin, and so I have the differential equation F=-k(x-x_0) \ddot{x}=-\frac{k}{m}x+\frac{kx_0}{m} Now, I get that I can...

Homework Statement Determine whether or not the following functions are harmonic: u = z + \bar{z} u = 2z\bar{z} Homework Equations z = u(x,y) + v(x,y)i \bar{z} = u(x,y) - v(x,y)i A function is harmonic if Δu = 0. The Attempt at a Solution Δu = Δz +Δ \bar{z} = u_{xx} + v_{xx} +...

Homework Statement Hello, I'm just curious as to whether I'm going about solving the following problem correctly... Problem Statement: A particle mass m and charge q is in the ground state of a one -dimensional harmonic oscillator, the oscillator frequency is ω_o. An electric field ε_o is...

Homework Statement Find the initial conditions for 2 interchangeable harmonic oscillators (undamped) so that they have the same amplitude of oscillation. Homework Equations x(t)=Xm*cos(wt+ϕ)The Attempt at a Solution The amplitude of the function is given by Xm so I would have thought that just...

Homework Statement Given a harmonic oscillator with mass m, and spring constant k, is subject to damping force F= cdx/dt and driven by an external force of the form F[ext]= FoSin(wt). A) Find the steady state solution. B) Find the amplitude and the phase. Homework Equations F=-kx the steady...

I seem to have two approaches that I've seen and understand, but I can't quite see how they relate. 1. Write a general time evolving state as a superposition of stationary states multiplied by their exp(-iEt/h) factors, and calculate <x>. We find that <x>=Acos(wt+b) as in classical physics (in...

Homework Statement If there are a large number of ions oscillating in a straight line, we can pick the nth one oscillating about its equilibrium a*n. The potential of the entire lattice is then U = 0.5*K[u(an)-u([n+1]a)]^2 - summed over all n. How do I use Force = -dU/du(an) to derive that...

Homework Statement A particle moves with simple harmonic motion in a straight line with amplitude 0.05 m and the period 12 s.Find (a) the maximum speed , (b) the maximum acceleration of the particle.Write down the values of the constants P and Q in the equation x/m = P sin [Q)(t/s)] Homework...

can we find the harmonic of vibration somehow just by knowing frequency?

Homework Statement I am curious as to how the second line in the equation is equal to the third line in the equation. The book my class is using is Taylor and it just skips so many steps. What happens to the sign, I know this must relate to euler in some way I am just not sure how. Thank you...

Homework Statement A 0.500Kg object is undergoing simple harmonic motion at the end of a horizontal spring with force constant k=300N/m. When the object is 0.012m from the equilibrium position, it is observed to have a speed of 0.300m/s. What is: a) The total energy of the object at any point...

Hello, I was just watching a youtube video deriving the equation for the Hamiltonian for the harmonic oscillator, and I am also following Griffiths explanation. I just got stuck at a part here, and was wondering if I could get some help understanding the next step (both the video and book...

Homework Statement A 50g mass is attached to a spring and undergoes simple harmonic motion. It's maximum acceleration is 15m/s and maximum speed is 3.5m/s. Determine a)angular frequency, b) spring constant, c) amplitude. Homework Equations ω = √k/m X(t) = A*cos(ωt + ∅) The Attempt at a...

Homework Statement Homework EquationsThe Attempt at a Solution Suppose mass of platform is ##M_1## and that of coin is ##M_2## . The normal force between them is N . EOM for platform (mass M1) = ##-kx+M_{1}g+N = M_{1}\ddot{x}## EOM for coin(mass M2) = ##M_{2}g-N = M_{1}\ddot{x}## This...

Hello, I juste don't know how this was done it is on the solutionnary of a very long exercise and i am not getting this calculation 1. Homework Statement <1,0| ax+ay++ax+ay+axay++axay|0,1> = <1,0|1,0> Homework Equations 3. The Attempt at a Solution We have that |0,1> = ay+ |0,0> I don't...

Hi, I have a few questions relating to the equation for maximum acceleration for SHM: amax = A (2 x pi x f)^2 where amax = max. acceleration, A = amplitude, f = frequency. How are these variables supposed to be interpreted when you relate them to each other. For example, is A inversely...

Hi everybody, I'm writing an exploration on the mathematics of simple harmonic motion and I stumbled across something I fail to understand in one of my resources (http://tutorial.math.lamar.edu/Classes/DE/Vibrations.aspx). In the example the author uses toward the end of the resource, the...