The figure shows the arrangement of three springs of different spring constant, connected to a mass m. When mass m oscillates find equivalent spring constant and the time period of vibration.

Explanation

In lower part, there are two springs of force constant 2k and k, connected in parallel. So, their effective spring constant is
`therefore k_(p) = 2k + k = 3k`
The arrangment is now simplified as show in figure.
Now we have two spring (each of force constant 3k) connected in series.
`therefore` Effective spring constant of the system is
`k_(s) = (k_(1)k_(2))/(k_(1) + k_(2)) = (3k xx 3k)/(3k + 3k) = (9k^(3))/(6k) = (3)/(2)k`
The time period is
`T = 2pisqrt((m)/(k_(s))) = 2pi sqrt((2m)/(3k))`.