What is Oscillator: Definition and 1000 Discussions
Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.
Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.
I have a Ti:Sapphire oscillator which outputs something like 25 fs pulses at 100 MHz (KM-labs if anyone is familiar). The laser has two curved mirrors on either side of the Ti:Sapphire which direct the fluorescence to the end mirrors. Once it is lasing in CW, you translate one focusing mirror...
I am thinking of using the output frequency of a 555 relaxation oscillator for measurement purposes. The frequency would be related to my measurement signal.
How stable are these oscillators at low frequencies?
Any personal experiences would help.
How stable can you get then with good...
Homework Statement
The period of a macroscopic pendulum made with a mass of 10 g suspended from
a massless cord 50 cm long is 1.42 s. (a) Compute the ground state (zero-point) energy. (b) If the
pendulum is set into motion so that the mass raises 0.1 mm above its equilibrium position, what will...
Homework Statement
http://img191.imageshack.us/i/questionyw.png/
Homework Equations
Given in problem
The Attempt at a Solution
a) I've been able to find expressions of operators x, p_x, y and p_y in terms of the creation/annihilation operators and hence been able to express the...
i have a quick question
A particle in ground state of a S.H.O whose potential is given by
V_1(X)=\frac{1}{2}mw^2_1x^2
suddenly changes to
V_2(X)=\frac{1}{2}mw^2_2(x-x_o)^2
what is the wavefunction going to be like for the new potential?
i'd think everything else stays the same in the...
Hello,
I want to find <xftf|x(t)|xiti> in harmonic oscillator.
I tried to insert the complete set of energy eigenstates to the right and the left side of x(t), but it yields somewhat more complicated stuff.
Thank you
Homework Statement
a block of mass m=.5kg is sliding on a horizontal table with coefficients of static and kinetic friction of .8 and .5 respectively. It is attached to a wall with a spring of unstretched length l=.13m and force constant 200 n/m. The block is released from rest at t=0 when...
Homework Statement
There is a block attached to the wall via a spring. The only damping force is friction, where there is kinetic and static.
Homework Equations
m(d^2x/dt^2)=-kx-?
The Attempt at a Solution
I can solve this, except usually the damping force is given as...
Homework Statement
a particle of mass m moving in one dimension has potential energy
V(x)=0.5m [[omega(subscript0)]^2] x^2
verify that
psi0 (proportional to) exp [(-m omega0 x^2)/2 h bar]
and
psi1 (proportional to) exp [(-m omega0 x^2)/2 h bar]
are both solutions of the time...
Homework Statement
I'm talking about the probability density plot of the harmonic oscillator. Is there some physical meaning to be extracted from this? Here's a link that contains the drawing of what I'm talking about http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc5.html...
Homework Statement
The problem can be found here. http://wopho.org/dl.php?id=17&dirfile=selection-problem/helical_rope.pdf" I am attempting to solve part 3. Homework Equations
The Lagrangian of the system is: L= \frac{m\dot{x}^2}{2}+\frac{mr^2\dot{\theta}^2}{2}-k \left(...
Homework Statement
The question states for a harmonic oscillator the wavefunction is:
\mu = C*x*exp(-\alphax2/2)
it then wants you to find \alpha.
using the standard hamiltonian:
H = -\hbar/2m d2/dx2 + 1/2 mw2x2
I have differentiated \mu twice and put it into the TISE.
for the left hand...
Homework Statement
A particle is in the ground state of a harmonic oscillator with classical frequency w. Suddenly the classical frequency doubles, w -> w' = 2w without initially changing the wavefunction. Instantaneously afterwards, what is the probability that a measurement of energy...
Homework Statement
A harmonic oscillator starts in its ground state (n=0) at t=-infinity. A perturbation H = -xF(t) is applied between t= -infinity and t = T.
(a) by considering the corresponding classical interaction explain why this represents the application of a time dependent force...
Homework Statement
We know that a particle in SHM is in a state such that measurements of the energy will yield either E_0 or E_1 (and nothing else), each with equal probability. Show that the state must be of the form
\psi = \frac{1}{\sqrt2} \psi_0 + \frac{e^{i \phi}}{\sqrt2} \psi_1
where...
Homework Statement
Hi guys. I've been working on this problem for a while, it's starting to frustrate me.
"Show that the function of Ѱ=e^(-bx^2) with b=mw/2ħ is a solution and that the corresponding energy is ħw/2."
Homework Equations
Schrodinger Eqn...
Hi can anybody explain to me how to calculate values for the resonant tank of the clapp oscillator. I know that capacitor in series with inductor sets the frequency. But I ve read that formula 1/Ceq = 1/c1+1/c2+ 1/cs, should be used to get Ceq which should be used for frequency setting. So what...
Homework Statement
In the time interval (t + δt, t) the Hamiltonian H of some system varies in such a way that |H|ψi>| remains finite. Show that under these circumstances |ψi> is a continuous function of time.
A harmonic oscillator with frequency ω is in its ground state when the stiffness of...
Is it necessary that force term in anharmonic oscillator should contain only third power in dependent variable(say x)? or any other higher power in dependent variable.
In the attached file, I have formulated a simple one dimensional harmonic oscillator and solved the model numerically. Such a model might represent a simple reaction coordinate along which a liquid drop actinide nucleus might split after absorbing a neutron. Clearly the complete model involves...
Hi, wondering if anyone can help with this;
we have the Hamiltonian of a linear harmonic oscillator
H=(p2+w2q2)/2
now we apply the frictional force F=ap(bq-1) where a and b are constants. how do we alter the Hamiltonian to take that into account?
if it helps, the total time derivative of H...
Hi, I've got a few questions about that common base colpitts oscillator. I am trying to simulate it but, I am not sure if the circuit is complete or is it missing anything? I have some formulas but not sure how to use them.I have some assumptions, are they right?
1. Capacitors R3 R4 nad R5...
I have designed an opamp based on thfollowing square wave setup http://www.national.com/ds/LM/LM124.pdf on page 11. I want to know what i would have to adjust to lower the frequency to the range of 10 hertz, it has a 5 volt input and the frequency range is at 10 Ghz I believe. any help would...
Hi, could anyone explain to me what the purpose of the each capacitor is in this common base colpitts?.
C1,C1,L are used to set the oscillation frequancy, right?
R1, R2,R3 are used to set the collector, base current and volatges, is that correct?
So what is the purpose of C3, C5 and C4...
uncertainty relation.
I think I'm on the right track.
Currently, I'm at,
E = (1/2m)*<p^2> + (1/2)*k*<x^2>
and when applying the uncertainty relation,
deltax = <x^2>^(1/2)
deltap = <p^2>^(1/2)
How do I go about connecting everything from here?
Thanks!
Homework Statement
A particle of mass m that is confined to a harmonic oscillator potential V(x) = \frac{1}{2} m \omega^2 x^2 is described by a wave packet having the probability density,
|\Psi (x,t) |^2 = \left(\frac{m\omega}{\pi\hbar} \right )^{1/2}\textrm{exp}\left[-\frac{mw}{\hbar}(x -...
Homework Statement
Verify that the ground state (n=0) wavefunction is an eigenstate of the harmonic
oscillator Hamiltonian. Using the explicit wavefunction of the ground state to calculate
the average potential energy <0|\hat{v}|0> and average kinetic energy <0|\hat{T}| 0>
Homework...
Homework Statement
The equation of motion of a forced undamped non-linear oscillator of unit mass is given by a+s(x)=Focoswt. Writing s(x)=s1x + s3x3, where s1 and s3 are constant, choose the variable wt= ϕ, and for s3<<s1 assume a solution
x=\sum(n=1 to ∞)(ancos[(n/3)ϕ]+bn sin[(n/3)ϕ])
to...
Homework Statement
A simple harmonic oscillator of force constant 2*106 N/m and amplitude .01 m has total maechanical energy 160 J...
Homework Equations
The Attempt at a Solution
Now this is not the question but what is the minimum potential energy...1/2kx^2 comes out to be...
1. Homework Statement
Show that bohr's hypothesis (that a particle's angular momentum must be an integer multiple of h/2pi) when applied to the three dimensional harmonic oscillator, predicts energy levels E=lh/pi w with l = 1,2,3. Is there an experiment that would falsify this prediction...
The TISE can be written as
-\frac{\hbar^{2}}{2m}\frac{d^{2}u}{dx^{2}} + \frac{1}{2}m\omega_{0}^{2}x^{2}u = Eu
Now my lecture notes say that it is convenient to define scaled variables
y = \sqrt{\frac{m\omega_{0}}{\hbar} x}
and \alpha = \frac{2E}{\hbar\omega_{0}}
Hence
\frac{d}{dx} =...
Homework Statement
In a reservoir there are three balls. There is a spring(the weight of spring is negligible) with elastic coefficient k between each two balls(small enough, like two particles). Suppose the center of gravity of the system does not move, and the mass of each ball is m. Suppose...
It is well known that for an isolated system, the normal mode frequency of a N-body harmonic oscillator satisfies Det(T-\omega^{2}V)=0. How about a non-isolated, fixed temperature system?
In solid state physics I have learned that in crystal the frequency does not change, but the amplitude of...
So, today while doing my homework for statistical mechanics I was reading about the quantum linear oscillator in the textbook, "Classical and Statistical Thermodynamics" by Ashley H. Carter. In it, after discussing the quantized energy it says:
"Note that the energies are equally spaced and...
Homework Statement
A particle mass m in the harmonic oscillator potential starts out in the state \psi(x,0)=A\left(1-2\sqrt(\frac{m\omega}{\hbar})x\right)^{2}e^{\frac{-m\omega}{2\hbar}x^{2}} for some constant A.
a) What is the expectation value of the energy?
b) At some time later T the wave...
Homework Statement
A particle in the ground state of the harmonic oscillator with classical frequency \omega, when the spring const quadruples (so \omega^{'}=2\omega) without initially changing the wave function. What is the probability that a measurement of the energy would still return the...
Homework Statement
A critically damped oscillator with natural frequency \omega starts out at position x_0>0. What is the maximum initial speed (directed towards the origin) it can have and not cross the origin?
Homework Equations
For the case of critical damping...
http://img707.imageshack.us/i/electronicsoscillator.jpg/
Dont know where to start for showing voltage difference at input is zero, suspose its something to do with non idealities of the op amp?
For the oscillator question , kinda know how its works; there's positive saturation giving...
I have a planar molecule with a torsional oscillation mode where it twists around a C-C bond by an angle \theta from some equilibrium position.
The restoring force is a function of theta, and the potential energy involved is given by V(\theta) = V_0(1-cos(2\theta))
I need to "use a Taylor...
Homework Statement
The particle with the mass m is in 2D potential:
V(r)=\frac{m}{2}(\omega_x^2x^2+\omega_y^2y^2),\quad \omega_x=2\omega_y,
and is described with wave package for which the following is valid: \langle x\rangle (0)=x_0,\ \langle y\rangle (0)=0,\ \langle p_x\rangle (0)=0\...
Homework Statement
The pendulum of a grandfather clock has a period of 1s and makes excursions of 3cm either side of dead centre. Given that the bob weighs 0.2kg, around what value of n would you expect its non negligible quantum amplitudes to cluster?
Homework Equations
[/B]
The...
Hi!
Info:
This is a rather elementary question about the creation a(+) and annihilation (a-) operators for the 1D H.O.
The problem is to calculate the energy shift for a given state if the weak perturbation is proportional to x⁴.
Using first order perturbation theory for the...
i am a last year EE student and I am creating a library in simulink. and at 1 stage i need to simulate a ring oscillator . i ve done it but with a lil bit of problems in the simulations. I am using spice parameters for simulink . that's why i asked if any of you guys have done it before.
how do...
Hello (this is not a homework)
I have a doubt about the ring oscillator. I have to create a R.O. with a frequency of 10kHz, now I know i have to link an odd number of inverters in a ring form, but using the formula of (f=1/2*n*Tp) it gives me a frequency in the Megas, I've red you can use a...
So here is the problem. A mass hanging from a spring is modeled by the operator L(y)=2y"+y'/10+2y (y=0 corresponds to hanging equilibrium). Assume mass starts with y(0)=1 and y'(0)=1. Assume an upward impulsive force of mag M is applied at the first possible time which results in complete end...
Homework Statement
Two masses attached via springs (see picture attachment). k_n represents the spring constant of the n^{th} spring, x_n represents the displacement from the natural length of the spring.
There are two masses, m_1 and m_2.2. The attempt at a solution
My problem is formulating...
Homework Statement
I need to find the time constant, tau,
Homework Equations
WILL EDIT THIS TOMORROW Bleeping FMS giving me major brainache *saddest face ever*
A(t) = A_0 times e^-t/tauThe Attempt at a Solution
I have had numerous attempts and I just fried my (fibromyalgic) brain out with...
Hello,
Attached are two problems I can not solve, thanks for the help.
The Attempt at a Solution
For the first question, I understand that I need insert A1coswt+A2sinwt into the homogenous equation , but don't know what's then ..
But I'm pretty much lost on both of em :(
Homework Statement
Ok so the question is, is the state u(x) = Bxe^[(x^2)/2] an energy eigenstate of the system with V(x) = 1/2*K*X^2 and what is the probability per unit length of this state.Homework Equations
The Attempt at a Solution So the way i did this was, to find if the state is an...