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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 =
F
g
+
F
s
+
F
d
+
F
e
=
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 di
ff
erential equation. Note that in general, if we
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- Spring '09
- EdrayGoins
- order differential equation
-
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