Simple harmonic motion — A/L Combined Mathematics

How do I practise Simple harmonic motion?

1 question with a worked solution

Check before you answer: Standard Differential Form: Establishing that the acceleration satisfies ẍ = -ω² x before citing SHM properties.

1. A particle moves in simple harmonic motion (SHM) defined by ẍ = -16x. If the amplitude of oscillation is A = 0.50 m, what is the maximum speed v_max of the particle?
   1. A) 1.0 m s⁻¹
   2. B) 8.0 m s⁻¹
   3. C) 2.0 m s⁻¹
   4. D) 4.0 m s⁻¹
   Check my answer

   Correct answer: C) 2.0 m s⁻¹

   Comparing ẍ = -16x with the standard SHM differential equation ẍ = -ω² x gives angular frequency ω = √16 = 4 rad s⁻¹. The maximum speed occurs at the equilibrium position (x = 0): v_max = ω A = (4 rad s⁻¹) × 0.50 m = 2.0 m s⁻¹.

   Show worked solution

   Step 1: Identify ω: ω² = 16 => ω = 4 rad s⁻¹. Step 2: Calculate v_max = ω · A = 4 × 0.50 = 2.0 m s⁻¹. Answer: 2.0 m s⁻¹.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Simple harmonic motion fit in the syllabus?

Year 2 · Term 3