Recent content by awelex

Hi, I'm trying to adapt the doppler shift formula for a stationary listener and a source traveling in a straight line towards/away from the listener to the case where the source does not move straight towards the listener. For example, suppose that I am looking north and train further in the...

A second after posting this, I think I figured it out: Since e^(-j*w*t) = cos(w*t) - j * sin(w*t), I'm missing a minus sign in my integral. Correct?

Hi, I have a general question regarding the computation of Fourier Series coefficients for real and odd inputs. In this case, the following should be true: ∫x(t)*e^(-j*k*w*t)dt = ∫x(t)*sin(k*w*t)dt However, every time I compute my coefficients this way, I get the inverse sign of what it...

Any takers? I found a case that clearly shows that the system is not time invariant, but I'd still love to know what is wrong about my proof. I can't seem to figure it out. Thanks!

Yes; no information at all is given about x(t).

Homework Statement Determine if the following system is time invariant: y(t) = x(t - 2) + x(2 - t) 2. The attempt at a solution I know from the solutions that the system is NOT time invariant, yet whenever I try to solve it I get the opposite result. Here's what I'm doing: y1(t)...

Alright, I'm giving it one more try. After I figured out how to deal with the t^2 part, I'm still stuck when it comes to solving the homogeneous equation: \left[ \begin{array}{c} x1' \\ x2' \\ x3' \end{array} \right] = \left[ \begin{array}{ccc} 0 & 1 & 0 \\ 0 & 1 & -1 \\ 1 & -1 & 0...

Well, I made some progress. I did manage to apply the method of undetermined coefficients to my system, which yielded two particular solutions, xp and yp. The total solution for y(t) and x(t) should then be y(t) = yh(t) + yp(t) x(t) = xh(t) + xp(t) with xh and yh being the solutions to...

I'm sorry if I seem thick, but how did you get this? And what is z in your system?

That's what I wanted to do, but there are two problems with this: a) the matrix P I get is singular and thus cannot be inverted b) It's not the procedure the book wants me to use, as the problem states I should use the method of undetermined coefficients. I suspect that I made an error earlier...

I did find the eigenvalues and eigenvectors, but how do I proceed from there?

I've just read the "must read" post and it seems that I should have posted my question in the homework section. If somebody could move it there, I'd appreciate it.

Hi, I've come across a problem in my differential equations book that I can't seem to be able to solve (it's not a homework problem, I'm just practicing): "Using matrix algebra techniques and the method of undetermined coefficients, find a general solution for x''(t) + y'(t) - x(t) +...

Hi, I'm being asked to test whether a function is of exponential order, i.e. whether abs( f(x) ) <= M*exp(a * t), for all t >= T (which is finite). The function is x * ln( x ). Now, I have the solution right here, so I know how to solve it. However, I did it a different way and wanted to ask...

Hi, I'm having peculiar difficulties with a rather easy integral, namely the integral of -sin(x) / (cos(x))^3. The problem is that depending on which integration technique I choose, I end up with two different result. Moreover, Mathematica gives me one of these two results, while the solution...