1. Find the equilibrium points for the following equations. Determine whether these equilibrium
points are stable, and, if so, nd the approximate angular frequency of oscillation
around those equilibria.
(i) d2y/dx2(x) = cosh(x) (ii) d2y/dx2(x) = cos(x) (iii) d2y/dx2 (x) = tan(sin(x)):
Hello, I'd like to know if I am proceeding correctly for the very first question, 1i.
A solution to i would be a equilibrium point if it is a constant solution.
Therefore, d2y/dx2(x) = cosh(x) = 0;
When with this equation, I get x = i(pi) / 2
Am I going the correct way? Can i(pi) / 2 be an answer? I haven't got a complex number for a solution before...
After that, for stability, I would just look at points of x near i(pi)/2.
points are stable, and, if so, nd the approximate angular frequency of oscillation
around those equilibria.
(i) d2y/dx2(x) = cosh(x) (ii) d2y/dx2(x) = cos(x) (iii) d2y/dx2 (x) = tan(sin(x)):
Hello, I'd like to know if I am proceeding correctly for the very first question, 1i.
A solution to i would be a equilibrium point if it is a constant solution.
Therefore, d2y/dx2(x) = cosh(x) = 0;
When with this equation, I get x = i(pi) / 2
Am I going the correct way? Can i(pi) / 2 be an answer? I haven't got a complex number for a solution before...
After that, for stability, I would just look at points of x near i(pi)/2.