Finding stability

Classical Mechanics Level 1

A particle is constricted to move along the positive $x$ -axis under the influence of a potential energy:

$U(x) = \frac{3}{x} + 7x$

Find the point of equilibrium for the particle. (Round your answer to three decimal places.)

1 solution

Tony Sprinkle
Jan 5, 2015

A point of equilibrium exists where $U'(x) = 0$ :

$U'(x) = -\frac{3}{x^2} + 7 = 0\quad\Rightarrow\quad x = \sqrt{\frac{3}{7}} \approx \boxed{0.655}$