Show that the 1 dimensional problem with equation of motion (FUNTION1) has a stable equilibrium point at x=1, and show that the period of small oscillations about the point is (FUNCTION2).
(PLEASE SEE ATTACHMENT FOR FUNCTIONS)
d^x/dt^2 = w^2*[1+2x-3x^2] = f(x)
Equilibrium point is given by,
f(x) = 0 ==> x = 1
also, f'(x) = ...
This is a proof regarding stable equilibrium points and small oscillations.