Force-Displacement (F-x) Graph:

• Area under F-x graph = Work done
• Positive area (above x-axis) = positive work
• Negative area (below x-axis) = negative work
• For spring: F = -kx is a straight line through origin; area = triangle = \frac{1}{2}$$kx^2

PE-Position (U-x) Graph:

• Slope = -F (force is negative of slope)
• Minima = stable equilibrium points
• Maxima = unstable equilibrium points
• Total energy line: E = KE + U. KE = E - U at any point
• Turning points: where E = U (KE = 0, body reverses)
• Body cannot exist where U > E (KE would be negative)

KE-Position Graph:

• For free fall: KE = $mgh_0$ - mgh = mg($h_0$ - h). Linear in h.
• For spring: KE = \frac{1}{2}$$mv_0^2 - \frac{1}{2}$$kx^2. Parabolic in x.