question_answer 5)

A particle is in linear S.H.M. 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 5 going towards A, (e) at 3 cm away from A going towards B, a (f) at 4 cm away from A going towards A.

Answer:

Refer to Fig 10 (NCT). 2, where A and 5 represent the two extreme positions of a S.H.M. For velocity, the direction from A to B is taken to be positive. The acceleration and the force .a long AP are taken as positive; and along BP are taken as negative. (a) At the end A, the particle executing S.H.M. is momentarily at rest being its extreme position of motion. Therefore, its velocity is zero; acceleration is +ve because it is directed along AP. Force is also +ive since the force is directed along AP, i.e., +ive direction. (b) At the end B, velocity is zero. Here, acceleration and force are negative as they are directed along BP, i.e., along negative direction. (c) At the midpoint of AB going towards A, the particle is at its mean position P, with a tendency to move along PA, i.e., -ve direction. Hence velocity is -ve. Both, acceleration and force are.wro. (d) At 2 cm away from B going towards A, the particle is at Q, with a tendency to move along QP, which is negative direction. Therefore, velocity, acceleration and force, all are negative. (e) At 3 cm away from A going towards B, the particle is at R, with a tendency to move along RP, which is positive direction. Here, velocity, acceleration and force, all are positive. (f) At 4 cm away from A going towards A, the particle is at S, with a tendency to move along SA, which is negative direction for velocity. Therefore, velocity is negative but acceleration is directed towards mean position, i.e., along SP, hence +ve. Similarly, force is also +ve.