The Attempt at a Solution
Suppose tension in the left string mAM be T1 and tension in the right string mBM be T2 .When the particles cross each other then the angle made by string mA and mB with vertical is α and that made by AM and BM be β . The speed of m is u and that of M is v .
The work done by tension would be zero , so
-(T1cosα)u + (T1cosβ)v - (T2cosα)u + (T2cosβ)v = 0
By symmetry I believe the tensions should be equal so if I put T1 = T2
I get , (cosα)u = (cosβ)v .
But now I do not think α is equal to β when the masses cross each other .
Am I thinking correctly ?