Ellen Says That Whenever the Acceleration Is Directly Proportional to the Displacement

Multiple Choice

Ellen says that whenever the acceleration is directly proportional to the displacement of an object from its equilibrium position, the motion of the object is simple harmonic motion. Mary says this is true only if the acceleration is opposite in direction to the displacement. Which one, if either, is correct?

A) Ellen, because ω² is directly proportional to the constant multiplying the displacement and to the mass.
B) Ellen, because ω² is directly proportional to the mass.
C) Mary, because ω² is directly proportional to the constant multiplying the displacement and to the mass.
D) Mary, because ω² is directly proportional to the mass.
E) Mary, because the second derivative of an oscillatory function like sin(ωt) or cos(ωt) is always proportional to the negative of the original function.