A particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?

For small displacements in a parabolic potential, the motion is Simple Harmonic Motion (SHM).The particle is released from rest at an initial displacement $x=A$.The equation for position is $x(t)=A\cos (\omega t)$.This corresponds to a cosine wave graph starting at the maximum positive displacement at $t=0$.