Work and energy

The elementary solution, you can calculate time, the equation of motion etc etc also:-
( ab is the unstreched spring at t=0, a'b is the streched spring at t=t )

at t=0 , V_m = -1 & V_b = 2
Suppose at time t=t, the extention in spring = x
=> displacement of m from t=0 will be 2*t - x , lets denote it by y ... this means V_m = dy/dt
=> dy/dt = 2 - dx/dt
=> d²y/dt² = - d²x/dt² ------- (1)

also d²y/dt² = kx/m -----------------(2)
=> d²x/dt² + kx/m = 0
=> x= A Sin(ωt) ... where ω=√k/m
=> dx/dt = Aω Cos(ωt)

now at t=0, y=0, x=0 & dy/dt=-1
this gives x_max = A = (2+1) * √m/k =0.6 m = 60 cm