Elastic force in string is conservative in nature .

`:.`       `W = Dela  u`

where  W = work  done by elastic force of string

     `Delta u` = Change in elastic potential  energy

`because `  ` W = - (u_f - u_i) = u_i - U_f`

or        `w = 1/2 kx^2 - 1/2 k(x + y)^2`

or        `w = 1/2kx^2 - 1/2 k(x^2 + y^2  + 2xy)`

           =     `1/2kx^2 - 1/2 kx^2 - 1/2ky^2 - 1/2 K( 2xy)`

           = ` - kxy - 1/2 ky^2`

           = `1/2 ky( - 2x - y)`

The work done against elastic force is

`w_(external) =  - w = (ky)/(2)  (3x + y)`