Simple Harmonic Motion — A/L Physics

How do I practise Simple Harmonic Motion?

1 question with a worked solution

1. A particle executes simple harmonic motion (SHM) with amplitude A and angular frequency ω. At what displacement from the central equilibrium position is the kinetic energy of the particle exactly equal to its potential energy?
   1. A) x = A / 4
   2. B) x = A / √2
   3. C) x = A / 2
   4. D) x = A / √3
   Check my answer

   Correct answer: B) x = A / √2

   Total mechanical energy in SHM is E = ½ m ω² A². Kinetic energy is KE = ½ m ω² (A² - x²) and Potential energy is PE = ½ m ω² x². Setting KE = PE gives A² - x² = x² => 2x² = A² => x = A / √2.

   Show worked solution

   Step 1: Set KE = PE: ½ m ω² (A² - x²) = ½ m ω² x². Step 2: A² - x² = x² => 2x² = A² => x² = A² / 2 => x = A / √2. Answer: x = A / √2.
   Modelled on: the A/L Physics examination pattern

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Where does Simple Harmonic Motion fit in the syllabus?

Unit 3.1 · Year 1 · Term 2