Particle in a Double Potential Well
This simulation shows a particle moving in a double-well potential \(U(x) = x^4 - 2x^2\). The left canvas shows the potential energy landscape with two minima at \(x = \pm 1\). The right canvas shows the phase space trajectory \((x, v)\).
With small damping, the particle can oscillate between the two wells. Adjust the damping constant to see the particle settle into one well. The phase trajectory is colored by speed.
\( \textcolor{midnightblue}{\textbf{Equation of Motion:}} \) \( \textcolor{maroon}{\ddot{x} + c \dot{x} + 4x(x^2 - 1) = 0, \quad x(0) = x_0, \quad \dot{x}(0) = v_0} \)
\( \textcolor{midnightblue}{\textbf{Potential Function:}} \) \( \textcolor{maroon}{U(x) = x^4 - 2x^2} \)
Double Well Potential Landscape
Phase Space Trajectory