Representing harmonic motion (10 minutes)

Notes on harmonic representations, including complex numbers reps_initcond_complexnumbers_wiki.ppt

  • Show a graph of an harmonic function, and define the amplitude, phase, frequency (cyclic and angular), period, etc. with reference to a prop - an oscillating mass perhaps.
  • Introduce the “A-form” \[f\left( t \right)=A\sin \left( \omega t+\varphi \right)\] (with which most students are familiar) and the “B-form” \[f\left( t \right)=B_{p}\cos \omega t+B_{q}\sin \omega t\] (with which many are not). Discuss which might be useful under different circumstances.
  • Don't derive a formal relationship between the arbitrary constants yet - let this follow from the initial conditions activity, which shows that the same motion can be represented both ways.
  • Make sure the students see the formal derivation of the connection after the activity.

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