AQA A Level Physics

Revision Notes

6.2.7 Energy in SHM

Energy in SHM

  • During simple harmonic motion, energy is constantly exchanged between two forms: kinetic and potential
  • The potential energy could be in the form of:
    • Gravitational potential energy (for a pendulum)
    • Elastic potential energy (for a horizontal mass on a spring)
    • Or both (for a vertical mass on a spring)
  • Speed v is at a maximum when displacement x = 0, so:

The kinetic energy is at a maximum when the displacement x = 0 (equilibrium position)

  • Speed v is 0 (and kinetic energy is 0) at maximum displacement x = A, so:

The potential energy is at a maximum when the displacement (both positive and negative) is at a maximum x = A (amplitude)

  • A simple harmonic system is therefore constantly converting between kinetic and potential energy
  • When one increases, the other decreases and vice versa, therefore:

The total energy of a simple harmonic system always remains constant and is equal to the sum of the kinetic and potential energies

Energy graph, downloadable AS & A Level Physics revision notes

The kinetic and potential energy of an oscillator in SHM vary periodically

  • The key features of the energy-time graph are:
    • Both the kinetic and potential energies are represented by periodic functions (sine or cosine) which are varying in opposite directions to one another
    • When the potential energy is 0, the kinetic energy is at its maximum point and vice versa
    • The total energy is represented by a horizontal straight line directly above the curves at the maximum value of both the kinetic or potential energy
    • Energy is always positive so there are no negative values on the y axis

 

  • Note: kinetic and potential energy go through two complete cycles during one period of oscillation
    • This is because one complete oscillation reaches the maximum displacement twice (positive and negative)

Energy graph with displacement, downloadable AS & A Level Physics revision notes

Graph showing the potential and kinetic energy against displacement in half a period of an SHM oscillation

  • The key features of the energy-displacement graph are:
    • Displacement is a vector, so, the graph has both positive and negative x values
    • The potential energy is always at a maximum at the amplitude positions xA, and 0 at the equilibrium position x = 0
      • This is represented by a ‘U’ shaped curve
    • The kinetic energy is the opposite: it is 0 at the amplitude positions xA, and maximum at the equilibrium position x = 0
      • This is represented by an ‘n’ shaped curve
    • The total energy is represented by a horizontal straight line above the curves

Exam Tip

You may be expected to draw as well as interpret energy graphs against time or displacement in exam questions. Make sure the sketches of the curves are as even as possible and use a ruler to draw straight lines, for example, to represent the total energy.

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