PHY354H1 Lecture Notes - Cytochrome C Oxidase Subunit I, Scientific Notation, Complex Differential Form
Document Summary
Kinematics of oscillations-continued: readings: supplementary notes handout, kinematics of oscillatory motion: phasor representation, constructive/destructive interference, commensurate frequencies, beats. z = rei form for describing oscillations, last time we worked on a new formalism for describing oscillations. The 1d oscillatory motion would be represented by circular motion in 2d where the new axis was the imaginary axis. We recover x by taking the real part of this: x = re(z) = re[aei( t+ )] = a cos( t + ): we can use the polar form to easily calculate derivatives. E. g. x"s velocity is v = re and a = re (cid:32) dz (cid:33) (cid:32) dv dt dt (cid:33) (cid:16) i aei( t+ )(cid:17) i2 2aei( t+ )(cid:17) For complicated di erential equations, the exponential notation can make solving the equation much simpler. We will see these when we get to the dynamics of oscillations. Phasor representation: notice that the exponential form could also be written: z = (aei )(ei t).
