*Answer:*
Let and represent the extensions of the first and second springs, respectively.
The net displacement of the mass from its equilibrium position is then given by

Let and be the magnitudes of the forces exerted by the first and second springs, respectively. Since the springs (presumably) possess negligible inertia, they must exert equal and opposite forces on one another. This implies that , or

Finally, if is the magnitude of the restoring force acting on the mass, then force balance implies that , or

Here, is the effective force constant of the two springs. The above equations can be combined to give

Thus, the problem reduces to that of a block of mass attached to a spring of effective force constant

The angular frequency of oscillation is immediately given by the standard formula

Hence, the period of oscillation is