Hooke's Law: How to find Amplitude

[Absent.Crisis]

Hello all,
(Newbie here so I hope I'm posting this in the right section, if not please guide me to the correct one)

I'm studying Hooke's Law in Physics and there is something I can't understand.
The equation for the Simple Harmonic Motion of a spring is given by $x'' + wx =0$

the general solution for the Differential equation above is given by: $A sin (wt) + B cos (wt)$

I came across a reference book that says: the amplitude is given by:
$sqrt {A^2 + B^2}$

I'd like to understand how they got this?? Right now I know that w is the angular frequency and wt gives the phase angle, but A and B as constants make no sense to me, what are they and what do they mean physically?

Any kind of answer would be greatly appreciated, please help me understand!
Thanks in advance!

 

[Doc Al]

A more recognizable form of the general solution would be this:
$$A\cos (\omega t + \phi)$$
Where A is the amplitude. Expand this (using a trig identity) and compare with the form you were given.

 

[Absent.Crisis]

Thanks a lot, I got it now :D