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Physics 235
Chapter 4

10

This differential equation is a nonlinear equation due to the sin
θ
term.
This equation has the
following general form:
x
=
−
c
x
−
sin
x
+
F
cos
ω
t
( )
Figure 10.
A damped pendulum, driven about its pivot point.
The solution to this equation can be studied using numerical methods, and we will focus on
the results obtained with Mathematica.
The code required to study the solutions of this equation
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Unformatted text preview: can be found in the file chaosPendulum in the Mathematica folder under Computing Tools on our website: (* Set the values of the various parameters *) c = 0.2; w = 0.694; F = 0.52; pi = N[Pi]; cycles = 50; steps = 30; (* Solve the differential equations with the given set of initial conditions. \...
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This note was uploaded on 01/08/2012 for the course PHY 235 taught by Professor Morgan during the Spring '09 term at SUNY Stony Brook.
 Spring '09
 MORGAN
 Physics

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