lecture_20 (dragged) 2

lecture_20 (dragged) 2 - MA 36600 LECTURE NOTES WEDNESDAY...

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Unformatted text preview: MA 36600 LECTURE NOTES: WEDNESDAY, MARCH 4 3 Newton’s Second Law of Motion states that F = m a. That is, m u￿￿ = sum of forces = Fg + Fs + Fd + Fe = m g − k (L + u) − γ u￿ + F (t) Since m g − k L = 0, we can rewrite this as m u￿￿ − k u − γ u￿ + F (t) =⇒ m u￿￿ + γ u￿ + k u = F (t). Hence the position u = u(t) satisfies a linear second order differential equation. Note that in general, if we have an equation in the form a y ￿￿ + b y ￿ + c y = f (t) where a, b, and c are constants, we identify m = a as the “mass,” γ = b as the “damping constant,” k = c as the “spring constant,” and F (t) = f (t) as the “external force.” ...
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