A spring of force-constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force-constant of

Length of first piece =l/3 Length of second piece =2 I I 3 By definition, a force of maguitude t is required to elonSate or compress the spring of length / by unity. So theelongationinthepieceoflength2llSwou\dbe2/3units. Now, for (2/3) unit elongatiotr, the force needed is k. So, for unit elongation.the force needed wold be  k(2/3)=3k2. This is force constant, by definition.