Infinite-Extent 2D Mass-Spring System vibration and dispersion relation

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M_Abubakr
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Hi,
I am trying to find equation of motion and its solutions for a 2D infinite lumped mass spring system as depicted in figure. All the masses are identical, All the springs are identical, and even the horizontal and vertical periodicity is the same n=a.
Mass-spring-system.png

I need to try find dispersive relation for such a system. Can anyone tell me how to solve this? I am fairly confident with mass-spring systems in one dimension with MDOF but I don't know how to solve this one and I can't find any similar problem solved over the internet.
 
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