Recent content by Slightly

I don't think that answers my question.

Below is a computer program for Mathematica that details how to calculate the Lyapunov exponent of a differential equation. What is the purpose of the code colored in red? ClearAll["Global`*"]; deq1 =-(y1[t]+ z1[t]); deq2 = x1[t]+0.1 y1[t]; deq3 =0.2+ x1[t] z1[t]-5.7 z1[t]; deq4 =-(y2[t]+...

That's exactly what I don't want. I'm trying to figure out how they get to the van der pol equation.

Yea, I tried plugging everything in like you just did, but I could not figure out how to get rid of the U^3 term.

Homework Statement Given characteristic equation for a circuit containing a diode, I must figure out how to fit a polynomial to the curve so that the van der pol equation is obtained. The paper I am reading is here: http://www.unige.ch/math/hairer60/pres/pres_rentrop.pdf My doubts are...

Homework Statement What are the possible degeneracies and what is the symmetry of the position probability distribution in the case of a particle subject to a three-dimensional potential with cubic symmetry?Homework Equations n/aThe Attempt at a Solution With a three-dimensional potential...

Update 1. Found that B = .15 by substituting σ1 for -σ2 and plugging in the values of 10^-4 and -10^-4 into the respective equations and added them.

Homework Statement In a silicon junction diode, the region of the planar junction between n-type and p-type semiconductors can be approximately represented as two adjoining slabs of charge, one negative and one positive. Away from the junction, outside these charge layers, the potential...

When solving a Fourier Series, you can run into things that have the following structure. cos(n*pi) cos(n*2pi) sin(n*pi/2) These expressions can be rewritten in terms of powers of -1 or as well as seeing that some terms drop to zero or are always the same value. cos(n*pi) =...

I was able to figure it out! Thanks.

I went through the DE and was able to obtain the characteristic equation to be r^2+cr/m + k/m = 0 I said k = - mg/a and c = mg/v_t so... r^2+gr/v_t - g/a = o In this case, can I assume r is the frequency? so, using the quadratic formula, r = -g/2v_t +/- sqrt(g^2/(4v^2)+ g/a) is this...

That's funny. So when I get the solution to the DE, where will the frequency come from?

Can you explain to me why you came to this conclusion? How is this system under-damped?

Homework Statement The terminal speed of a freely falling object is v_t (assume a linear form of air resistance). When the object is suspended by a spring, the spring stretches by an amount a. Find the formula of the frequency of oscillation in terms of g, v_t, and a. Homework Equations the...

Here is the picture!