Recent content by chilge

Hi vela, I only know how to solve the matrix problem numerically. Do you know how I can get an analytical solution with matrix methods?

Hi pasmith, Thank you for your suggestion! That did the trick, and I was able to come up with a solution for ##x(t)## and ##y(t)##. I forgot to mention in my problem statement that ##f=2\Omega##, so the characteristic equation ##k^2+ifk-\Omega^2## has a double root, and the solution is of the...

Hi Ray, Thank you for your suggestion! It's been quite awhile since I've seen Laplace transforms and had forgotten about them. Unfortunately I ran into a bit of trouble when trying to find a solution... ##{\cal L}\{x(t)\}=X(s)## ##{\cal L}\{\frac{dx}{dt}\} = sX(s) - x(0) = sX(s)## (with the...

Homework Statement I need to (analytically) solve a system of coupled second-order ODEs: (A) \frac{du}{dt} - fv = \Omega^2x (B) \frac{dv}{dt} + fu = \Omega^2y where u = \frac{dx}{dt} v = \frac{dy}{dt} subject to the initial conditions u(t=0) = U and v(t=0) = 0. Homework Equations --- The...

Hi Chet, thank you very much for your reply - it helped get me out of my rut and thinking in a new way. Here's what I've come up with: We've already found that x(t)=C2eat y(t)=C3e-at Let's say that the particle is at (x0,y0) at t=0. Then x(t)=x0eat y(t)=y0e-at Therefore we can find out where...

I accidentally posted this to the "Calculus & Beyond" forum when I meant to post it to the physics forum. If someone can tell me how to move this post, I will get rid of it here! Homework Statement Consider a property, for example temperature θ, that is conserved during advection (i.e. Dθ/Dt =...

Homework Statement I have a function y that is axisymmetric, so that y=y(r). I want to solve for r such that ∇2y(r) = Z. Can anyone tell me if I'm following the right procedure? I'm not sure since there are two "∂/∂r"s present... Homework Equations ∇2 = (1/r)(∂/∂r)(r*(∂/∂r)) +...

Homework Statement A signal E(t) is made up of three terms, each having the same frequency but differing in phase: E(t) = E0cos(ωt) + E0cos(ωt + δ) + E0cos(ωt + 2δ) It is possible to find the amplitude of the sum vector by summing each vector described as a magnitude multiplied by a...