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Q13.2: NCERT Physics - Part 2 OSCILLATIONS 13.2 Solution: Which of the following examples represent (nearly) simple…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students often label any periodic motion as simple harmonic, overlooking that SHM requires a linear restoring force (force ∝ displacement) and a single sinusoidal mode. Verify that the motion is to‑and‑fro about an equilibrium with $F=-kx$ (or its small‑angle equivalent) before calling it SHM.
Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? (a) the rotation of earth about its axis. (b) motion of an oscillating mercury column in a U-tube. (c) motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point. (d) general vibrations of a polyatomic molecule about its equilibrium position.
Step-by-Step Verified Solution
**Answer:** (b) and (c) are simple harmonic motion. (a) and (d) are periodic but not simple harmonic.
**Step-by-Step Explanation:**
(a) The rotation of the earth about its axis is periodic but not simple harmonic because it is not to-and-fro motion about a fixed point [citation:10].
(b) In an oscillating mercury column in a U-tube, the mercury moves to and fro on the same path about the fixed position. Hence, it is simple harmonic motion [citation:10].
(c) When a ball bearing is released from a point slightly above the lowermost point of a smooth curved bowl, it moves to and fro about the lowermost point. Hence, it is simple harmonic motion [citation:10].
(d) A polyatomic molecule has many natural frequencies of oscillation. Its vibration is a superposition of individual simple harmonic motions. Hence, it is periodic but not simple harmonic [citation:10].
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