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Grade 11IIT JEE Entrance Exam

A rectangular slab of sides a and b is suspended from a ceiling by two parallel strings of Length L each. The seperation between the strings is d. The plate is displaced slightly in its plane keeping the strings tight. Show that it will execute simple Harmonic Motion and find its time period. - Sir I solved it using Torque equation about the point at the ceiling about which centre of mass rotates. In doing so, parameters a and b are also coming. But they are nowhere in the answers. Please help.

Profile image of Deepal
8 Years agoGrade 11
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1 Answer

Profile image of Arun
6 Years ago
Solution :- Here we have to consider oscillation of centre of mass
 
Driving force F = mgsin¢
 
For small angle ¢ , sin¢ =¢
 
•°• a = g¢ = g(x/L) [where g and L is constant ]
 
•°• a proportional x
 
so the motion is simple harmonic
 
Time period , T = 2π√dispalcement / acceleration
 
T = 2π √x/(gx/L)
 
T = 2π√L/g Answer