Cracking the SAT Physics Subject Test

force exerted by the springs would be

F 1 + F 2 = −k 1 x + −k 2 x = −(k 1 + k 2 )x

Since Feff = −(k 1 + k 2 )x, we see that keff = k 1 + k 2.

(b) Imagine that the block was displaced a distance x to the right of its
equilibrium position. Then the force exerted by the first spring would be F 1 =

−k 1 x and the force exerted by the second spring would be F 2 = −k 2 x. The net

force exerted by the springs would be

F 1 + F 2 = −k 1 x + −k 2 x = −(k 1 + k 2 )x

As in part (a), we see that, since Feff = −(k 1 + k 2 )x, we get keff = k 1

+ k 2.

(c) Imagine that the block was displaced a distance x to the right of its
equilibrium position. Let x 1 be the distance that the first spring is stretched,

and let x 2 be the distance that the second spring is stretched. Then x = x 1 + x 2.

But x 1 = −F/k 1 and x 2 = −F/k 2 , so