Explain why the total mechanical energy of an object undergoing simple harmonic motion remains constant, and describe how the kinetic and potential energies vary during one complete oscillation.

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 of mass m oscillates on a frictionless horizontal surface, attached to a spring. The object passes through the equilibrium position with maximum speed and momentarily comes to rest at the amplitude positions.

Model answer (4 marks)

In the absence of friction or other dissipative forces, no energy is transferred to the surroundings, so the total mechanical energy is conserved and remains constant.

At the equilibrium position the displacement is zero, so the spring potential energy is minimum (zero) and the kinetic energy is maximum.

At the amplitude positions the displacement is maximum, the velocity is zero, so the kinetic energy is minimum (zero) and the potential energy is maximum.

During the oscillation energy is continuously converted between kinetic and potential forms, but their sum – the total mechanical energy – stays the same throughout the cycle.

Examiner tips

  • State that no energy is lost to the surroundings; this shows conservation of mechanical energy.
  • Describe the energy at the two key points (equilibrium and amplitude).
  • Explain the continuous conversion between KE and PE.
  • Use correct terminology: kinetic energy, potential energy, total mechanical energy, conservation.

Common mistakes

  • Claiming that potential energy is non‑zero at equilibrium; it is zero for a spring with zero natural length.
  • Confusing maximum kinetic energy with maximum potential energy; they occur at opposite positions.
  • Ignoring the role of friction or other dissipative forces in the conservation statement.

Mark scheme (4 marks)

  1. In the absence of friction (or other dissipative forces), no energy is transferred to the surroundings, so total mechanical energy is conserved/constant.
  2. At the equilibrium position, displacement is zero so potential energy is at a minimum (zero), and kinetic energy is at a maximum.
  3. At the amplitude (maximum displacement) positions, the velocity is zero so kinetic energy is zero/minimum, and potential energy is at a maximum.
  4. During the oscillation, energy is continuously and repeatedly converted between kinetic and potential forms such that their sum (total mechanical energy) remains constant throughout.

Key terms in this question

simple harmonic motion · total mechanical energy

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