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.
Answer:
From above figure, where A and B represent the two extreme positions of a SHM. 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 alsong Bp 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 becaue 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, accleration 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 psoiton P, with a tendancy to move along PA. Hence, velocity is positive. Both accleration and force are zero.
(d) At 2 cm away from B going towards A, the particle is at Q, with a tendancy to move along QP, which is negative direction. Therefore, velocity, acceleration and force all are positive.
(e) At 3 sm away from A going towards B, the particle is at R, with a tendancy to move along RP, which is positive direction. Here, velocity, acceleration all are positive.
(f) At 4 cm away from A going towards A, the particles is at S, with a tendancy to move along SA, which is negative direction. Therefore, velocity is negative but acclereation is directed towards mean position, along SP. Hence it is positive and also force is positive similarly.
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