Combinations of Springs Springs in Series - Consider two springs with force constants k1 and k2 connected in series supporting a load F = mg. - Let the force constant of the combination be represented by k - For the combination, supporting the load F=mg: k1 F = kx ( where x = the total stretch ) and x= F k - For each spring - the bottom supports mg=F and stretches by x1 F = k1 x1 k2 F or x1 = k1 - the top spring support mg plus the weight of the bottom spring (which is negligible Thus F is the stretching force for both springs) F = k2 x2 or x2 = m F k2 F = mg - The total stretch x = x1 + x2 and or F F F = + k k1 k2 1 1 1 = + k k1 k2 Springs in Parallel - Consider two springs with force constants k1 and k2 connected in parallel supporting a load F = mg. - Let the force constant of the combination be represented by k - For the combination supporting the load F=mg: k1 k2 F = kx ( where x = the total stretch ) - The two individual springs both stretch by x but share the load (F = F1+F2) and F1 = k1 x while F2 = k2 x - Thus the total force is F = F1 + F2 or F2 F2 m kx = k1 x + k2 x F = mg and k = k1 + k2