# Equilibrium Points

Equilibrium Points

Shows three different values for  superposed on the plot of the same potential energy function U(x). Let us see how they would change the situation. If  (purple line), the turning point shifts from XI to a point between XI and X.Also. at any point to the right of . the system’s mechanical energy is equal to its potential energy; thus, the particle has no kinetic energy and  no force acts on it, and so it must be stationary.

Next consider the particle’s behavior if (green line). If we place it at  it is stuck there. It cannot move left or right on its own because to do so would require a negative kinetic energy. If we push it slightly left or right, a restoring force appears that moves it back to A particle at such a position is said to be in stable equilibrium. (A marble placed at the bottom of a hemispherical bowl . If we place the particle in the cup like potential well centered at X. it is between two turning points. It can still move somewhat, but only partway to X.