Answer
(a) The restoring force is $3F$ when the spring is stretched to a length of 13 cm.
(b) The restoring force is $2F$ when the spring is compressed to a length of 8 cm.
Work Step by Step
The magnitude of a spring's restoring force is $F = kx$, where $x$ is the length that the spring is stretched or compressed. The problem statement tells us that the restoring force is $F$ when $x = 1~cm$.
(a) The restoring force is $3F$ when the spring is stretched 3 cm. That is, the restoring force is $3F$ when the spring is stretched to a length of 13 cm.
(b) The restoring force is $2F$ when the spring is compressed 2 cm. That is, the restoring force is $2F$ when the spring is compressed to a length of 8 cm.
