Final answer:
A displacement of 1 cm produces the smallest restoring force according to Hooke's Law, since the force required is directly proportional to displacement.
Step-by-step explanation:
The displacement value that will produce the smallest restoring force when the same spring is used in each case is a displacement of 1 cm. In Hooke's Law, the restoring force is directly proportional to the displacement from the spring's equilibrium position, represented by the equation F = -kx. Here, 'F' stands for the restoring force, 'k' is the spring constant, and 'x' is the displacement. The negative sign in the equation indicates that the restoring force is in the direction opposite to the displacement. So, the smaller the displacement, the smaller the restoring force will be.