A rectangular plate of sides a and b is suspended from a ceiling by two parallel strings of length L each in the figure. The separation between the strings is d. The plate is displaced slightly in its plane keeping the strings tight. Show that it will execute harmonic motion. Find the time period.

Answer

B

Explanation

Here we have to consider oscillation of centre of mass.
Driving force, F=mg sin theta`
Acceleration =a=s/m=gsintheta`
`:. A=gtheta=g(m/L)`
[wehre g and L and const].
`:. A alpha x `
So the motion is simple Harmonic.
`Time period `t=2pisqrt(displacement/Acceleration)`
`=2pi sqrt(x/(gx/L))=2pi sqrt(L/g)`