Question

Three identical springs each have the same spring constant k. if these three springs are attached end to end forming a spring three times the length of one of the original springs, what will be the spring constant of the combination?

Answer 1

If the springs are connected together from end to end, they are arranged in series. For springs in series, the forces are additive. 

Spring 1: F1 = k1(Δx1)
Spring 2: F2 = k2(Δx2)
Spring 1: F3 = k3(Δx3)

Total Force = k1(Δx1)+k2(Δx2)+k3(Δx3)
Total Force = (k1+k2+k3)(Δx,total)

The spring constants are added together and multiplied with the total length of elongation to find the total force acting on it.