# Dynamics

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)

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#### Solution Preview

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) = ...

#### Solution Summary

This is a proof regarding stable equilibrium points and small oscillations. The dimensional problems with equation of motion are examined.

$2.19