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Q13.5: NCERT Physics - Part 2 OSCILLATIONS 13.5 Solution: A particle is in linear simple harmonic motion between two…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students often incorrectly assume that acceleration and force align with the direction of velocity, but in SHM, the restoring force always points toward the mean position regardless of whether the particle is moving toward or away from it. Always determine the sign of acceleration based on the particle's displacement from the center, not its current direction of motion.
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.
Step-by-Step Verified Solution
**Answer:** (a) v = 0, a = +, F = + (b) v = 0, a = �, F = � (c) v = �, a = 0, F = 0 (d) v = �, a = �, F = � (e) v = +, a = +, F = + (f) v = �, a = +, F = +
**Step-by-Step Explanation:**
Let O be the midpoint (mean position), A and B the extremes.
(a) At end A: Particle is momentarily at rest, so . Acceleration and force are directed towards O (positive direction), so , [citation:13].
(b) At end B: Particle is momentarily at rest, so . Acceleration and force are directed towards O (negative direction), so , [citation:13].
(c) At midpoint O going towards A: Velocity is along negative direction, so . At mean position, , [citation:13].
(d) At 2 cm from B going towards A: Velocity is towards A (negative direction), so . Acceleration and force are directed towards O (negative direction), so , [citation:13].
(e) At 3 cm from A going towards B: Velocity is towards B (positive direction), so . Acceleration and force are directed towards O (positive direction), so , [citation:13].
(f) At 4 cm from B going towards A: Velocity is towards A (negative direction), so . Acceleration and force are directed towards O (positive direction), so , [citation:13].
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