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Oscillations: Two General Approaches
Someone hands you a system that oscillates, and asks you to ﬁnd the equation
of motion. What are you going to do? Well, here are two methods that I ﬁnd
useful for solving these things:
Forces
•
Draw a picture of the system
•
Identify the oscillating object and draw a Free Body Diagram (FBD) for
it
•
Write out Σ
F
=
m
a
for the object
•
Rearrange this equation to obtain a diﬀerential equation to your liking
•
Propose a trial solution (
x
(
t
)) to the equation, something that oscillates 
you expect it to have a
cos
(
ωt
+
δ
) piece
•
Run your solution through the diﬀerential equation  this will usually give
you values for
ω
, and sometimes other constants
•
Evaluate your solution at some time (usually
t
= 0) where you have some
information about displacement, speed, etc. in order to ﬁnd solutions for
the other constants (typically the amplitude and phase shift)
Energy (Most useful if
W
NC
= 0
)
•
Draw a picture of the system
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 Spring '11
 Corbin
 Physics, Force

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