a) Zero, Positive, Positive
b) Zero, Negative, Negative
c) Negative, Zero, Zero
d) Negative, Negative, Negative
e) Zero, Positive, Positive
f) Negative, Negative, Negative

Explanation:

The given situation is shown as:

A particle is in linear simple harmonic motion between the endpoints A and B.

(a) At the extreme point A, its velocity is zero As the particle is at rest momentarily at point A.

Its acceleration is positive as the direction of the acceleration of the particle is towards B and force is also positive.

(b) At point B, the particle is at rest again for a moment. Hence, its velocity is zero at B.

Its acceleration is negative as the direction of the acceleration of the particle is towards A and force is also negative.

(c)

Its velocity at the mean position O is the maximum. The value for velocity is negative as the particle is directed leftward. The acceleration and force of a particle executing SHM is zero at the mean position.

(d)

The particle is moving toward point O from the end B. This direction of motion is from A to B. Hence, the particle’s velocity and acceleration, and the force on it, all are negative.

(e)

The particle is moving toward point O from the end A. This direction of motion is from A to B. Hence, the values for velocity, acceleration, and force are all positive.

(f)

This case is similar to the case given in (d).