Explain how the velocity and kinetic energy of an object undergoing simple harmonic motion (SHM) vary as the object moves from its equilibrium position to a position of maximum displacement.

IB DP Physics Standard Level (2023 syllabus) — C.1 Simple harmonic motion · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

An object oscillates in simple harmonic motion about a fixed equilibrium position.

Model answer (4 marks)

At the equilibrium position the velocity is at its maximum value. As the displacement increases towards the maximum displacement, the restoring force does negative work on the object, so the velocity decreases to zero at the maximum displacement. Kinetic energy, which is proportional to the square of the velocity (Ek = ½mv²), is therefore maximum at the equilibrium position and decreases to zero at the maximum displacement as the kinetic energy is transferred to potential energy, while the total mechanical energy remains constant.

Examiner tips

  • Use the key phrases "maximum velocity at equilibrium" and "velocity decreases to zero at maximum displacement".
  • Explain the energy transfer from kinetic to potential energy to show conservation of mechanical energy.
  • Show the relationship Ek = ½mv² to link velocity and kinetic energy.

Common mistakes

  • Confusing the positions of maximum velocity and maximum displacement.
  • Failing to mention that kinetic energy is zero at maximum displacement.
  • Not linking the decrease in kinetic energy to the increase in potential energy.

Mark scheme (4 marks)

  1. At the equilibrium position the velocity is at its maximum value.
  2. As displacement increases towards maximum displacement, the restoring force does negative work on the object, so velocity decreases to zero at maximum displacement.
  3. Kinetic energy is proportional to the square of velocity (Ek = ½mv²), so kinetic energy is also maximum at equilibrium.
  4. Kinetic energy decreases to zero at maximum displacement as kinetic energy is transferred to potential energy, with the total mechanical energy remaining constant.

Key terms in this question

simple harmonic motion · equilibrium position · maximum displacement · kinetic energy

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