Analyzing SHM with Two Pendulums and Varying Masses

[Dinheiro]

Homework Statement

In a thread with a sphere of mass M on one end, another thread BC is suspended with a sphere of mass m (as the image below). The point A executes small oscillations in the horizontal of period T. Find the length L of BC, knowing that B remains straight underneath A at all time

Homework Equations

SHM and dynamics equations

The Attempt at a Solution

As AB is always on the vertical, we can see that when A is pushed to one side, BC hangs to the same side in order to balance the angular momentum. So, adopting the non inertial reference of AB, the sphere of mass m is now affected by the weight and the force that pushed A, let's say F. Then I've tried to analyze the forces in the direction of the mass' m movement to prove the simple harmonic motion of the system. But how can I calculate F? I can't seem to describe it mathematically :/

 

[BvU]

AB remains always on the vertical

confuses me no end. Can I interptret this as: B remains straight underneath A at all time?

 

[Dinheiro]

Yes, this is what you should interpret, actually. Let me edit the post

 

[BvU]

So for all I kn
ow AB could just as well be a stiff bar, right ?

 

[Dinheiro]

Yes, despise their mass and consider they are a stiff bar

 

[BvU]

BC can be any length at all, there's nothing to restrict it: nothing is being said about C !

 

[Dinheiro]

Probably not. Imagine, for an instance, |BC| >> |AB| and m>>M, then the period of oscillation must be smaller to compensate the angular momentum and to keep AB in the vertical. So I guess there must be a relation between the masses, period and BC's length as the problem requests