Reading x, v, and a

Simple harmonic motion is one function and its derivatives. The position is x(t) = A cos(ωt + φ); differentiate once for the velocity and twice for the acceleration. Each derivative brings down a factor of the angular frequency ω and shifts the phase a quarter cycle, so the velocity peaks at Aω and the acceleration at Aω², always pointing back toward equilibrium as a = -ω²x. The phase constant φ is fixed by where the motion starts.

Two things slip most often: the chain rule and the phase. Differentiating a cosine or sine multiplies it by ω every time, so dropping that factor is the most common slip. The phase constant φ is fixed by the starting position together with the direction of motion, not free to set to zero. And the three curves never line up — the velocity runs a quarter cycle ahead of the position, while the acceleration sits exactly opposite it.