Amplitude of a simple harmonic motion equation

[nehcrow]

if you have the equation: x(t) = Acos(ωt + ϕ)

and you have the following information: A 200 g block hangs from a spring with spring constant 10 N/m. At t = 0s the block is 20 cm below the equilibrium position and moving upward with a speed of 100 cm/s.

The answers give a short method of calculating the amplitude but I have no idea how the reached it, basically what they did was: A = sqrt((x0)^2 + (v0/ω)^2)
how did they reach that conclusion??

 

[rl.bhat]

velocity v = dx/dt = -Aωsin(ωt + φ)
Square both the sides and simplify.

 

[nehcrow]

Thanks!