Simple harmonic motion on a vertical line — A/L Combined Mathematics

How do I practise Simple harmonic motion on a vertical line?

1 question with a worked solution

1. A light elastic spring hanging vertically is extended by an equilibrium length e = 0.098 m when a mass m is gently attached to it. The mass is then pulled down slightly and released. Taking g = 9.8 m s⁻², what is the period of the resulting vertical oscillations?
   1. A) 0.50 s
   2. B) 1.0 s
   3. C) 0.10π s
   4. D) 0.20π s (approx 0.628 s)
   Check my answer

   Correct answer: D) 0.20π s (approx 0.628 s)

   At vertical equilibrium, string tension equals weight: k e = m g => k / m = g / e. The angular frequency of small vertical oscillations about this equilibrium point is ω = √(k/m) = √(g/e) = √(9.8 / 0.098) = √100 = 10 rad s⁻¹. Period T = 2π / ω = 2π / 10 = 0.20π s ≈ 0.628 s.

   Show worked solution

   Step 1: Formula: T = 2π √(e / g). Step 2: T = 2π √(0.098 / 9.8) = 2π √(0.01) = 0.20π s ≈ 0.628 s. Answer: 0.20π s (approx 0.628 s).
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Simple harmonic motion on a vertical line fit in the syllabus?

Year 2 · Term 3