What is the formula for displacement in simple harmonic motion?

Simple harmonic motion response is sinusoidal with a frequency of $omega$, so the general case is expressed as $$x=Asin(omega t+phi)=Acos(omega t-pi/2+phi)$$ or $$x=Bsin(omega t)+Ccos(omega t),$$

where $A$ is the amplitude, $phi$ is the so-called phase angle (whose negative, $-phi$, is called the phase delay), and $B$ and $C$ are constants related to the amplitude and phase angle through

$$A^2=B^2+C^2$$ and $$B=cosphiqquad C=sinphiqquadphi=tan^{-1}(C/B)$$ (where the arctangent is limited between $-pi/2$ and $pi/2$). You can find these constants from the boundary conditions. If $x=0$ at $t=0$ (i.e., the displacement is zero at time zero), for example, then we have simply $x=Asin(omega t)$. If instead $dot x=dx/dt=0$ at $t=0$ (i.e., the speed is zero at time zero), then $x=Acos(omega t)$. Does this make sense?