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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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- Spring '09
- EdrayGoins
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