IB Physics HL Theme C: Wave behaviour questions

Answer: A. For simple harmonic motion, the graph of $a$ against $x$ is a straight line through the origin with gradient $-\omega^2$ From $T=2.0\ \text{s}$ $\omega=2\pi/T=\pi\ \text{rad s}^{-1}$ so the required gradient is $-\pi^2\approx-9.87\ \text{s}^{-2}$ Trace P has this negative gradient and passes through the origin.
B: uses a negative gradient through the origin, but its magnitude is about $3.14\ \text{s}^{-2}$ confusing $\omega$ with $\omega^2$
C: has the required gradient but does not pass through the origin, so acceleration is not proportional to displacement.
D: has a positive gradient, so acceleration is in the direction of displacement rather than towards equilibrium.
Remember: SHM requires acceleration to be proportional to displacement and opposite in direction.