Why ? recall (where k is the spring constant). x=0 is the equilibrium position,and +ve x is towards extension (to right, here). Restoring force . force pushes object back to original position. Period t is time for one complete cycle of the motion; related to frequency f (in cycles/sec, or rev/sec) by: = ka2 ie. the total energy in a harmonic oscillator is proportional to the the oscillation. = k xmax2 = mv2 + kx2 v2 = (2e kx2)/m = (ka2 kx2)/m = (k/m) (a 2 -x 2 ) = (ka2/m) (1- (x2/a2) ) A is the amplitude, in meters, is the max distance from equilibrium. Giancoli example 11-4: spring stretches 0. 150 m when a 0. 300 kg mass is lowered gently on it. spring is then setup horizontally with the same mass on a frictionless table, and pulled 0. 100 m from the equilibrium point. = vmax [ (a2 x2) / a] v = vmax (1 (x2/a2) )