In a spring-mass system the length of the spring is L and it has a mass M attached to it and oscillates with angular velocity w .the spring is then cut into two parts,one(A) with relaxed length aL and other(B) with relaxed length(1-a)L.The force constants of the two springsAandB are

Using k₁l₁ = k₂l₂ ,

we get          

and 

as

Put the above value of k in the values of k' and k'' to get your answer