Two masses with a spring on a incline

Two blocks A and B with the same mass m=1kg connected by a massless spring with Elastic coefficient k=200N/m are on a smooth(i.e. no frictions) incline with angle θ=30° ，as the picture shown,where C is a fixed plate. Initially,the system is rest.Now give a Force F paralleled to the incline upwards on the block A ,in order to make A move upwards with constant acceleration .When the block B is just exactly leaving the plate C,the magnitude of F is equal to 2mg . Find the total time T(in seconds) that F acting on A before B leaves the plate C . (g=9.8m/s^2)

Bonus ：Find the general formula for the total time T with arbitrary m,k,g and θ .