MTH 425 Lecture Notes - Lecture 15: Angular Frequency, G2 Phase
Document Summary
Equilibrium dy d 2y dt 2 + b. Ics: y (0) = y0, y (0) = v0 y m. Undamped and unforced vibrations f (t) 0, Let c2 = a cos and c1 = a sin (c2,c1) Y = a sin cos t + a cos sin t. Damped free vibrations m d 2y dt + ky = 0 aux. eq n : mr 2 + br + k = 0 r = b dt 2 + b dy. 2m case b2 < 4mk (under damped oscillatory motion) b2 4mk < 0. 4mk b2 y = e b. 2m t(c1 cos t+c2 sin t) y = ae b. 2m t y damping factor sin( t + ) A exp(-b/2m t) case b2 > 4mk (over damped) r1. Y = c1e r1t + c2e r2t y is not sinusoidal (no oscillations), damping is too strong y y or t r1.
