How Does Earth's Rotation Affect Plumb Bob Deflection?

[Anisotropic Galaxy]

Due to Earth's rotation, a plumb bob may not hang exactly along the direction of the Earth's gravitational force on the plumb bob but may deviate slightly from that direction. (a) show that the deflection \thetais given by \theta = (\frac{2\pi^2R}{gT^2})sin(2L), where R is the radius of the Earth and T is the period of the Earth's rotation.

This problem is very hard. I try to get a = \frac{2\pi(RcosL)^2}{T^2RcosL} and then must get F so I try to separate the thingie into components byut then Fx and Fy get into a mess and I'm confused. Help!

Thanks

 

[Tide]

I am not sure what you tried but you need to find the direction of the tension in the wire supporting the bob which you can determine from the local direction of the gravitaional force (directed toward the center of the Earth) and the centripetal force (directed toward Earth's the axis of rotation). I presume your L is the latitude \lambda.