Recent content by Forcefedglas

My example found was of the form x_1(k+1) = G_1x_1(k)^2+G_2x_1(k)+G_3x_2(k) \\ x_2(k+1) = G_4x_2(k)^2+G_5x_2(k)+G_6x_1(k) To find the singular points, I set x1(k+1) = x1(k) and x2(k+1) = x2(k) to give a set of two simultaneous quadratic equations. Solving these said equations simultaneously in...

I understand how to find the eigenvalues, the problem is that I need to find 2 functions such that when solved for its singular points (by setting xn(k+1) = xn(k)), the Jacobian matrix has four pairs of eigenvalues (to do this the functions will have to be at least quadratic, and solving them...

Homework Statement Give an example of a non-linear discrete-time system of the form x1(k + 1) = f1(x1(k), x2(k)) x2(k + 1) = f2(x1(k), x2(k)) With precisely four singular points, two of which are unstable, and two other singular points which are asymptotically stable. Homework Equations J =...

Thanks, it all makes a lot more sense now. One of the goals was also to minimize the set of sampled sinusoids - I'm guessing I take a N-point DFT and keep reducing N until it's barely within specifications. EDIT: One more thing though, what's the relevance of point 2 (You may rely on the...

Homework Statement Homework Equations I'm guessing trigonometric identities such as sin(a)cos(b) = 1/2(sin(a+b)+sin(a-b)) might be relevant. The Attempt at a Solution I've been thinking of some way to get an approximation of each harmonic by working with the Fourier series representation...

Homework Statement Homework EquationsThe Attempt at a Solution I know what the transients should generally look like, the only part that's throwing me off is how to model the intended load voltage of 18V. I'm guessing that when the switch is on (after transients) the load voltage will be close...

Thanks that clears up a lot, strange that I never specifically heard about this in any of my introductory circuit courses but it makes sense now.

Ah ok, so the equivalent capacitances (and the voltages across them) combine and since Vgs2=-Vgs1, the current sources are equivalent and one can be removed? So whenever there's a wire connecting two portions of a node like this, can you always just remove it and proceed to simplify the circuit...

Homework Statement I've found the gain, but now I need to estimate the upper cutoff frequency with the open circuit time constant method, so the upper 3dB cutoff would roughly be $$\sum_{i = 1}^{n} \frac{1}{\tau_i}$$ The attempt at a solution I'm currently trying to make sense of the given...

Guess the given answer must be off then, thanks for clearing that up.

I fixed up most of the errors I think (left i component in terms of z and x since it goes to 0 anyway). The x component was supposed to be ##z^2-x##. Would the correct normals in the x=0 and x=3 planes be the unit vector i at x=3 and -i at x=0?

Homework Statement Evaluate ##\int\int_S \textbf{F}\cdot\textbf{n} dS ## where ##\textbf{F}=(z^2-x)\textbf{i}-xy\textbf{j}+3z\textbf{k}## and S is the surface region bounded by ##z = 4-y^2, x=0, x=3## and the x-y plane with ##\textbf{n}## directed outward to S. The attempt at a solution I've...

Oh ok, strange that the question suggested for me to do so then. Either way, thanks for all the help.

Ah ok I think I understand now, I found the angle of intersection by setting ##4cos\phi=2##, giving ##\phi=\pi/3## , so the integral becomes ##\int_{0}^{2\pi}\int_{0}^{\pi/3}\int_{0}^{2} \rho^2sin\phi d\rho d\phi\ d\theta + \int_{0}^{2\pi} \int_{\pi/3}^{\pi/2} \int_{0}^{4cos\phi} \rho^2sin\phi...

Yeah I know something's off with my bounds but I'm not sure how to get the correct bounds in this case; or how to switch around the iterated order like the question suggests.