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

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

1 question with a worked solution

Check before you answer: Hooke's Law Formulation: Stating T = λx / l accurately with correct extension expressions.

1. A particle of mass m = 0.20 kg attached to an ideal horizontal spring of stiffness k = 20 N m⁻¹ oscillates without friction on a smooth horizontal table. What is the period T of oscillation?
   1. A) 0.20π s (approx 0.628 s)
   2. B) 1.0 s
   3. C) 0.40π s
   4. D) 0.10π s
   Check my answer

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

   For a mass-spring system in horizontal SHM, the restoring force is F = -kx = m ẍ => ẍ = -(k/m) x. Angular frequency is ω = √(k/m) = √(20 / 0.20) = √100 = 10 rad s⁻¹. The period of oscillation is T = 2π / ω = 2π / 10 = 0.20π s ≈ 0.628 s.

   Show worked solution

   Step 1: Formula: T = 2π √(m / k). Step 2: T = 2π √(0.20 / 20) = 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 horizontal line fit in the syllabus?

Year 2 · Term 3