Ellen says that whenever the acceleration is directly proportionalto the displac

Question

Ellen says that whenever the acceleration is directly proportionalto the displacement of an object from its equilibrium position, themotion of the object is simple harmonic motion. Mary says this istrue only if the acceleration is opposite in direction to thedisplacement. Which one, if either, is correct?
Ellen, becausew2 is directly proportional to the constantmultiplying the displacement and to the mass.
Ellen, becausew2 is directly proportional to themass.
Mary, becausew2 is directly proportional to the constantmultiplying the displacement and to the mass.
Mary, becausew2 is directly proportional to themass.
Mary, because thesecond derivative of an oscillatory function like sin(wt)or cos(wt) always is the negative of the originalfunction.

Explanation / Answer

option E is correct because displacement and acceleration should be proportional andshould lie in opposite directions are the essential conditions forthe motion should be simple harmonic.

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