The springs in figures A and B are identical, but the spring in A has three times the length of each spring in B. Find the ratio of periods Tₐ/Tᵦ.

Question

G1 Physics · Accepted Answer

For a uniform spring, spring constant is inversely proportional to length. If each short spring in B has constant k, the spring in A, being three times longer, has k/3. The three springs in B are parallel, so their effective stiffness is 3k. Therefore Tₐ/Tᵦ=√[3k/(k/3)]=3. Correct answer: C.