An assembly of identical spring mass systems is placed on a smooth horizontal surface( there are 2 blocks each connected with a spring which are attached to the opposite walls and the blocks of mass m each just touch each other). Initially the springs are relaxed. The left mass is displaced to the left while the right mass is displaced to the right and released. The resulting collision is elastic. The time of oscillation of the system is?

Hint: based on symmetry you know the center of the middle spring doesn't move. It therefore acts as if that point is fixed to a wall. Hence each mass is essentially connected to a full spring on one side and half spring on the other. The spring constant of the half spring is twice the value of the full-length spring.

Or you can set up the system of ordinary differential equations that define the movement of both masses and solve for intial conditions.