Simple Harmonic Motion - Particle Projection

Question

Given $x=A\cos(\omega t) + B\sin(\omega t)$, how do you find the values of constants $A$ and $B$? I am aware that that depends on initial conditions, but I am unsure of the how. The initial conditions are $x(0)=2$ and $x'(0)=0$.

Answer 1

The first initial condition gives you : $2=A\cos(0) + B\sin(0)$

The second initial condition gives you : $0 = -2A\omega\sin(0)+B\omega\cos(0)$

Hence $A$ and $B$.