Question
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.
Solution
From above figure, where A and B represent the two extreme positions of a Simple Harmonic Motion. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along B are taken as negative.
(a) At the end, A, the particle executing SHM is momentarily at rest being its extreme position of motion. Therefore, its velocity is zero. Acceleration is positive because it is directed along AP, Force is also Positive since the force is directed along AP.
(b) At the end B, velocity is zero. Here, acceleration and force are negative as they are directed along BP.
(c) At the mid-point of AB going towards A, the particle is at its mean position P, with a tendency to move along PA. Hence, velocity is positive. Both acceleration and force are zero.
(d) At 2 cm away from B going towards A, the particle is at Q, with a tendency to move along QP, which is the negative direction. Therefore, velocity, acceleration, and force all are positive.
(e) At 3 cm away from A going towards B, the particle is at R, with a tendency to move along RP, which is a positive direction. Here, velocity, acceleration all are positive.
(f) At 4 cm away from A going towards A, the particles are at S, with a tendency to move along SA, which is the negative direction. Therefore, velocity is negative but acceleration is directed towards the mean position, along SP. Hence it is positive and also force is positive similarly.
