Response function Definition and 22 Threads

$$<H(\omega)>=\sum_{j} χ_{HAj}h_j(\omega)$$ Where $$χ_{HA}=\frac{1}{2\hbar} Tr{{\rho}[{H(t)},{A(0)}]}$$. But $$[H(t),A(0)]=[H_o,A(0)]-[A(t)h,A(0)]=-h_0 cos(\omega t)[A(t),A(0)]$$. So $$χ_{HA}=-\frac{1}{2\hbar}Tr(\rho h_0 cos(\omega t)[A(t),A(0)])=-h_0cos(\omega t)χ_{AA}$$. Then...

In particular I'm studying the paper "Theory of dynamic response functions of periodically modulated physical systems" by Lovesey et al. and "modulated system" are mentioned many times. My thesis advisor recommend to me reed this paper but is very confuse, any reference you can give me in...

I was reading the book "finite temperature field theory" (https://www.amazon.com/dp/0521820820/?tag=pfamazon01-20) and encountered a problem on page 111 about linear response theory. Consider a system with some conserved baryon matter perturbed by a source J_\mu, coupled to the baryon current...

Homework Statement The acceleration amplitude of a damped harmonic oscillator is given by $$A_{acc}(\omega) = \frac{QF_o}{m} \frac{\omega}{\omega _o} \sqrt{\it{R}(\omega)}$$ Show that as ##\lim_{\omega\to\infty}, A_{acc}(\omega) = \frac{F_o}{m}## Homework Equations $$\it{R}(\omega) =...

Homework Statement Locate the poles of the response function \alpha(\omega) in the complex plane for an LRC circuit. Homework Equations \alpha(\omega)=\frac{-i\omega}{L}\frac{1}{\omega_0^2-\omega^2-i\omega\gamma} \omega_0^2=\frac{1}{CL} \gamma=\frac{R}{L} The Attempt at a Solution So we've...

Ive read other threads on here about this and am still slightly confused about it. I did a little experiment; and I am hoping someone can help shed some light on the results. The experiment: 1. Create a system: modeled after a simple spring-mass-damper with mass=1 damping zeta=.1, natural...

Suppose we represent the input information as a (nx1) column vector, the output information as another (nx1) column vector and the system response function as a (nxn) matrix. My question, is it possible to calculate the values of the cells of the matrix knowing the input and the output? For...

Hi, I'm analyzing a 3 dof undamped system with discrete springs and masses. Three of the springs have time-dependent stiffness, following periodic law (with period T), they are modulated at the same frequency but with a phase difference of 120 deg one from the other. So this is my system: (M *...

Homework Statement I have a problem where the circuit is as follows: (pic attached I hope) but if you can't see it it's just a power source (AC), resistor and inductor with 2 terminals across the inductor (from were you measure the voltage). I want to derive the response function, and I am...

Hi everyone, I'm a new member but it's not the first time I look at the forum. Well, I don't know if this is the right section to post my question. I think it is related to quantum mechanics interpretation too. Anyway, let's have a look at my problem. I've computed cross section for photon...

I attempted by inputting u(τ-t)u(t-τ) into the second part of the integral. Since I want to change the second part of the integral to go from [+∞, -∞]. And as for first part of the integral I added a u(t-τ) term after the x(τ) to change the integral from [t,-∞] into [+∞, -∞]. I am not sure if I...

I undestand the following concerning the frequency response function; Frequency response function is a fundamental measurement that isolates the dynamic properties of a mechanical structure. It describes the input output relation between two points of a structure as a function of...

for a given spring/damper system the equation of motion is: [PLAIN]http://img600.imageshack.us/img600/2140/equation1.png where x is the displacement of a mass from a fixed point d is a damping constant L1 and L2 constant lengths k1 and k2 are 2 spring constants...

This isn't really a homework question but I felt this is the most relevant section for this. I therefore apologize for not following the standard post template. I was going through my electrical engineering notes on frequency response functions. It was explaining how to plot frequency response...

I am trying to find the frequency response function given the input and output spectra from the picture i got that X(iw) = iU(w)U(2-w) - iU(w+2)U(w) and that Y(iw) = iwU(w)U(1-w) - iwU(w+1)U(w) So H(iw) = Y(iw)/X(iw) and H(iw) = wU(1-w) - wU(w+1) / U(2-w) - U(w+2) i am having...

EM response function of the "Phase Action" of a BCS superconductor Hello, I am looking for a paper in which people calculated the EM response of phase action of A BCS SC. In the book "Condensed Matter Field Theory" by Altland and Simons, on page 393 they mention such a thing in the discussion...

i am given the Laplace transform of an impulse response function, as well as its input. i am supposed to find its output. H(s) = 1/s2 + s + 1 x(t) = sin2(t-1)U(t-1) what i have done so far is the following: i know that Y(s) = H(s)X(s) and from this i can easily find y(t) so i found X(s)...

Hi, given the state equations of a system, x(dot) = Ax + Bu y = Cx is the impulse response function of this system C(e^(At))B? If not, how can i identify the impulse response from a given state equations? Please advise. Thank you.

Hi looking for some help on the below I'm a little bit stuck. The effect of an earthquake on an elevated water tank is to be investigated. The water tank has mass m=2x10^6 kg and natural frequency wn=10.6 rad/s and a damping coefficient of 12% critical damping. Ground acceleration can be...

Hello Can anybody please help me to perform a Frequency Response Function analysis in ANSYS many thanks in advance

Homework Statement The relationship between the input voltage V(t) and the output voltage across a resistor VR(t) is:- CR dVR /dt + VR = CR dV/dt Circuit diagram of a capacitor and resistor with VR(t) in series across V(t) 1. Show that the frequency response function G(iw) (w= omega)...

I have a damped linear oscillator, originally at rest in its equilibrium position [therefore, x(0)=0 and x'(0)=0]. It is subjected to a forcing function: F(t)/m = {0, if t<0 {a(t/tau), if 0<t<tau {a, if t>tau I have to find the response function. However, when I attempt to find the step...