Module 6.4 “Euler’y Method,”

Repeat the exercises of Module 6.2. “Euler’y Method,” using the Runge-Kutta 4
method. Compare the relative errors with those of the corresponding exercises from
Module 6.2. ° Ruler’s Method.” and Module 6.3, “Runge-Kutta 2 Method.”

6. Download the file simplePendiulim from the text’s website in one of the sys-
tem dynamics tools. Figure 3.3.3 of Module 3.3. “Tick Tock—The Pendu-
lum Clock.” shows a plot of a simple pendulum’s angle. angular velocity,
and angular acceleration versus time that is the result of the simulation with
Ar= 0.01 and Runga-Kutta 4 integration. Run the simulauon with Ar = 0.01
using. in turn, Runga-Kutta 4+. Runga-Kutta 2. and Euler’s methods or what-
ever methods are available with your system dynamics tool. Describe any
anomalies in the graphs. Repeat the simulations and description for Ar = 0.1.
Discuss the implications of your findings.