F-x Graph: Area under curve = work done. For spring: triangular area = \frac{1}{2}$$kx^2.

U-x Graph (PE diagram): The most powerful qualitative tool. Force F = -dU/dx (negative slope). Equilibrium where slope = 0. Stable equilibrium at PE minima ($d^{2U}$/$dx^2$ > 0). Unstable at PE maxima.

Total energy E = KE + U is a horizontal line on the U-x graph. KE = E - U at any position. The body oscillates between turning points where E = U (KE = 0). Region where U > E is forbidden (KE cannot be negative).

Spring-mass system: U = \frac{1}{2}$$kx^2 is a parabola. At x = +/-A (amplitude): KE = 0. At x = 0: KE maximum. At x = A/2: PE = E/4, KE = 3E/4.