Question
Which of following conditions are not sufficient for simple harmonic motion? Explain:
(a) Acceleration ∝ displacement.
(b) Force acting on particle should be directed towards mean position.
Solution
(a) Acceleration is directly proportional to displacement. But for a motion to execute S.H.M, the direction of acceleration must be directed towards mean position is not indicated here.
Therefore thiscondition is not sufficient for the particle to execute simple harmonic motion.
(b) Force is directed towards mean position and hence the acceleration. But this does not give the variations of acceleration w.r.t. displacement.
Therefore this condition is also not sufficient.
But both the conditions jointly are sufficient for simple harmonic motion.
