Recent content by JuanYsimura

Homework Statement Consider the system x' + x = F(t), where F is smooth, T-periodic function. IS it true that the system necessarily has a stable T-periodic solution x(t)? If so, Prove it; If not, find an F that provides a counterexample. Homework Equations x' + x = F(t) The...

I have the folloring problem: Given the following flow on the torus (θ_1)' = ω_1 and (θ_2)' = ω_2, where ω_1 /ω_2 is irrational then I am asked to show that each trajectory is DENSE. So I need to prove that Given any point p on the torus, any initial condition q, and any ε > 0, then there...

Homework Statement For two equal-amplitude waves of nearly equal frequencies w+d/2 and w-d/2 (at a fixed position x), you have shown that the intensity exhibits \beats" which for d = 2pi Hz can be perceived directly by the ear, even though the main frequency is perceived only through the...

1. Homework Statement Write a wave in one space dimension as ARe(ei(kx-wt-d))where A is the amplitude of the wave. Find a second wave of the same frequency such that the sum of the two vanishes at x = 0 and x = L. Assuming the wave velocity c = w/|k| is fixed, for what frequencies ! is...

Homework Statement Write a wave in one space dimension as ARe(ei(kx-wt-d))where A is the amplitude of the wave. Find a second wave of the same frequency such that the sum of the two vanishes at x = 0 and x = L. Assuming the wave velocity c = w/|k| is fixed, for what frequencies ! is this...