Rectangular plate SHM

1. The problem statement, all variables and given/known data

A rectangular plate of sides ‘a’ and ‘b’ is suspended from a ceiling by two parallel strings of length L each. The separation between the strings is ‘d’. The plate is displaced slightly in its plane keeping the strings tight. Find the time period of SHM.

2. Relevant equations

3. The attempt at a solution

I have drawn two rough sketches depicting the orientation of the plate while in motion.Not sure which one correctly describes the situation .In the first picture the side ‘b’ always remain horizontal while in 2nd picture the side ‘b’ makes an angle θ with the horizontal.θ is the angle which strings make with the vertical.

I think the 1st picture is correct . In that case the plate is not rotating about the CM and the plate can be simply replaced by its CM .

The CM is at a distance L+a/2 from the ceiling .

The time period will be 2π√(L+a/2)/g But this is incorrect .

I would be grateful if somebody could help me with the problem.

Attached Images
File Type: gif plate.GIF (1.7 KB)
File Type: gif plate1.GIF (3.1 KB)

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