{{page>wiki:headers:hheader}}



===== Representing harmonic motion (10 minutes) =====


Notes on harmonic representations, including complex numbers {{courses:lecture:oslec: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.

{{page>wiki:footers:courses:osfooter}}