PHY354H1 Lecture Notes - Angular Frequency, Lincoln Near-Earth Asteroid Research, Simple Harmonic Motion
Document Summary
Oscillations in phase space and dynamics: readings: for oscillation dynamics: morin 4. 2, simple harmonic motion examples. Simple harmonic motion: last time: we studied how to solve linear second order homogeneous. Odes: standard example: mass on a spring with no damping or driving forces: (1) m x + kx = 0, tried a solution of the form x = ae t where a and are unknowns, found: (cid:115) K m: we learned nothing about a, but we now have 2 possible solutions for. ode theory says that a linear homogeous 2nd order ode will have. The nal solution is the superposition of these 2 solutions. So: (cid:104)(cid:16)(cid:113) k m (cid:17) (cid:105) (cid:104) (cid:16)(cid:113) k (cid:17) m (cid:105) t x(t) = a exp t. + b exp for some a and b are constants which can be determined by the initial conditions: for our speci c example, k/m < 0. So we could right the exponential (cid:20)(cid:18)(cid:113) (cid:19)
