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

The force constant of a spring is inversely proportional to its length. If a spring of length L is cut into two pieces of lengths x and (L-x), such that
$x=2(L-x)\text{ or }x=\frac{2L}{3},$
then the force constant of the spring of length x is related to the force constant k of the complete spring of length L as
$\frac{k_1}{k}=\frac{L}{x}=\frac{L}{2L/3}=\frac{3}{2}\text{ or }{k}_1=\frac{3}{2}k$