Oscillations of a complicated spring block system

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Homework Statement


A 4kg block M in horizontal plane is attached to a sprig S1 fixed to a light rod OA of length 4m as shown in diagram(refer to attachement). The other end O of the rod is hinged to rotate in the plane about the vertical axis passing through it. A spring S2 is fixed to the mid point B of the rod. If the spring constants of both springs are k=10N/m then calculate the angular frequency of oscillations of the mass.


Homework Equations





The Attempt at a Solution


Firstly i am a little confused about the plane of the rod....If the axis is vertical i am assuming it is in the horizontal plane....Anyway i dont think it has any effect on the sum....

Nw coming to my attempt....I didnt go too far.....Correct me wherever i am wrong....

Since in these cases we assume the displacement to be very small i am assuming that the diaplacement of the block and the extensions of the springs to be parallel (ie i am neglecting the curve of the arc)....
Let extensions of :
Spring S1 be x1 and that of spring S2 be x2.....and let displacement of block from mean position be x....

Then x= (x1)+2*(x2)....Hope i am correct till this....

What to do after this ? because of the rod i am having difficulty in finding the force on the block....

I feel it should be kx1....But then i dont have any other relation to get x1 or x2.....

How to go about furthur? Please help.....
 

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