SHM

take the tension in string with mass to be =T
so the springs will get '2T' each
hence is m is pulld by 'x'

x=2x₁+2x₂ ......(net extension due to each spring)......(1)

and 2T = k₁x₁=k₂x₂.........(2)

put the vlues of x1and x2 in \(1)....

to get

x=4Tk1+4Tk2

put the values ..x=3T/2k.....get k(effective)
..and put in time period...
i hope u got it....THANKS FOR THE QUESTION

another simple method for solving, assume that u have displaced the block downward by some distance x, then extension of both springs will be x/2 this mens that both springs are in parallel, so the k eff. = 8k/3 , now from constraint relation, if tension on block is T , then tension in spring will be 2T and extension x/2, so using these conditions in designing equivalent spring - mass system 2T = 8k/3 * x/2

=> T = 2kx/3 or time period of SHM is 2pi sqrt( 3m/2K )

thanks...