Springs in Series and Parallel

The following table gives formulas for the spring that is equivalent to a system of two springs, connected either in series or in parallel, whose spring constants are k1 and k2. Here C stands for compliance which is equal to 1/k i.e. reciprocal of spring constant. The same formulas can be extended to the systems of more than two springs.

Now consider a spring with spring constant equal to k. We can say that the spring is made from two small springs each with spring constant 2k connected in series.

So here we can conclude that when a spring with spring constant k is divided into two equal parts the spring constant of each part will be 2k. To generalize it, we can say that when a spring with spring constant k is divided into n equal parts the spring constant of each part will be nk. Where n=2,3,4,…