Two springs of spring constants k1 and k2 are joined in series. The effective spring constant of the-combination is given by:

Let us consider two springs of spring constants k1 and k2 joined in series as shown in the figure.Under a force F, they will stretch by y1 and y2.So y = y1+y2or Fk  = F1k1+F2k2but as springs are massless, so force on them must be the same, i,e., F1 = F2 = FSo, 1k = 1k1+1k2     or  k = k1k2k1+k2Aliter: In series combination,1kS = 1k1+1k2 = k2+k1k1k2     ⇒kS = k1k2k1+k2