Answer to Question #224331 in Classical Mechanics for yesuf

Question

The potential energy function for a system is given by U(x) = -x3 + 2x2 + 3x.
Determine the force Fx as a function of x.
For what values of x is the force equal to zero?

Answer 1

$F(x)=U'(x)=-3x^2+4x+3,$

$F(x)=0,$ where

$x_{1,2}=\frac{2±\sqrt{13}}3,$

$x_1≈-0.54,$

$x_2≈1.87.$