A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is

(a) at the end A,

(b) at the end B,

(c) at the mid-point of AB going towards A,

(d) at 2 cm away from B going towards A,

(e) at 3 cm away from A going towards B, and

(f) at 4 cm away from B going towards A.

Let us analyse each case: Refer the figure above.

(a) At the extreme position A, the velocity is zero, acceleration and force are directed towards the mid point O and are positive.

(b) At the end B, another extreme position, velocity is zero, acceleration and force are directed towards O and are negative.

(c) Here, the velocity is negative and maximum. Acceleration and force are zero.

(d) Velocity, acceleration and force are negative as they travel in the negative direction.

(e) Velocity is positive. Acceleration and force are directed towards O and are positive.

(f) Velocity is directed along BA, hence it is positive. Acceleration and force are directed towards OB and are positive.

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