Elasticity

In this problem, we have two spring systems: the first system with spring constant and the second system with two springs in series, each with spring constant . When two springs are arranged in series, the equivalent spring constant is given by: Thus, the equivalent spring constant for the second system is: Now, according to Hooke's Law: For the first system, the force required to stretch the spring by is: For the second system, since the equivalent spring constant is , the stretch for the same force is: Equating the forces in both systems, , we get: Solving for : Thus, the stretch for the second system is .