Question

For a particle executing simple harmonic motion, the acceleration is proportional to
(a) displacement from the mean position
(b) distance from the mean position
(c) distance traveled since t=0
(d) speed

Answer 1

Answer ⇒ Option (a). Displacement from mean Position.

Explanation ⇒ In Simple Harmonic Motion,

Force is linearly proportional to the negative of the displacement.

∴ Acceleration is also proportional to negative of linear displacement.

Now, Displacement in the Simple Harmonic Motion is always measured from the mean position. Therefore,  Option (a). will be correct.

Displacement from the mean position is the shortest distance and acceleration is proportional to the shortest distance only. Distance may be large, thus (b). and (c). and (d). options are incorrect.

Hope it helps.

Answer 2

Option (a). Displacement from mean Position.

Explanation ⇒ In Simple Harmonic Motion,

Force is linearly proportional to the negative of the displacement.

∴ Acceleration is also proportional to negative of linear displacement