Question

What is the frequency w of SHM simple harmonic motion of two masses coupled by three springs horizontally on a frictionless surface.

Two mass three spring system.
Assume k1 = k2 = k3 = k.
m1 = m2 = m.

Answer 1

Here there are two masses which can oscillate in two different ways. Both moving in the same direction at any point t of time. Or both moving in opposite directions at any point. So two SHM possible with different frequencies.

w = w0 = sqrt(k/m) for in phase SHM.

w = w0* sqrt3 = sqrt(3 k/ m).

See enclosed pictures for equations of motion and solutions.