As illustrated in the figure, a rectangular plate with sides a and b hangs from a ceiling via two parallel strings, each having a length L . The distance separating the strings is d . If the plate is given a small displacement within its plane while ensuring the strings remain taut, it performs simple harmonic motion. Determine the time period of this motion.

Step-by-step solution

When the rectangular plate is given a small displacement within its plane such that the strings remain taut, the two strings, the ceiling, and the top edge of the plate form a parallelogram. Because the opposite sides of this linkage are equal (the strings both have length L , and the distance between them is d at both the ceiling and the plate), the plate undergoes pure translational motion without any rotation. Its orientation remains horizontal throughout the motion. Since the plate translates purely, every poin