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.

Question

Quizplus · Accepted Answer

For simple harmonic motion, the acceleration must be directly proportional to the displacement and opposite in direction, which is why Mary is correct. The second derivative of functions like sin(ωt) or cos(ωt) is proportional to the negative of the original function, indicating this opposite direction relationship.

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