F=ma 2024 Problem 20

Physics · mechanics

Problem

Question: As shown in the figure, four massless rigid rods are connected into a quadrilateral by four hinges. The hinges have mass

m

, and allow the rods to freely rotate. A spring of spring constant

k

is connected across each of the diagonals, so that the springs are at their relaxed length when the rods form a square. Assume the springs do not interfere with each other. If the square is slightly compressed along one of its diagonals, its shape will oscillate over time. What is the period of these oscillations? (A)

2\pi \sqrt{\frac{m}{4k}}

. (B)

2\pi \sqrt{\frac{m}{2k}}

. (C)

2\pi \sqrt{\frac{m}{k}}

. (D)

2\pi \sqrt{\frac{2m}{k}}

. (E)

2\pi \sqrt{\frac{4m}{k}}

. *Note: This problem references figure(s): `image_question/F=MA_2024_20_1.png`*

Browse the problem library