18.03 Lecture Notes - Lecture 13: System Of Linear Equations, Linear Combination, Hypotenuse
Document Summary
I drew the spring/mass/dashpot system and added a force to it: the little sail comes back into play. mx" + bx" + kx = f_ext (*) Notice by the way that i can put the damper on the left in parallel with the spring: it still opposes velocity. If x" < 0 , f_dash > 0 and so on: so you get exactly the same equation. Also important will be the "associated homogeneous equation" mx" + bx" + kx = 0 (*)_h which we know all about after lecture 12. We can "reduce" this by dividing by m: x" + (b/m)x" + (k/m) = 0. If b = 0 we get solutions with circular frequency sqrt(k/m) . If b > 0 , you get exponentially damped sinusoids, with smaller circular frequency omega_d (or not oscillating at all, if b is big enough).
