Case-Study No. 1

Solve this equation numerically using:
Central Difference Method (Time steps: τ_n/20 and τ_n/40) [20%]
Required: Hand Calculations for two iterations + computer code

4th-order Runge-Kutta method, (Time steps: τ_n/20 and τ_n/40) [20%]
Required: Hand Calculations for two iterations + computer code

MATLAB built-in functions [10%]

Plot displacement, velocity, and acceleration as a function of time from 0 to 1min. Initial conditions θ(0)=π/6 and θ ̇=0 [20%]
Report Format (Cover page, Table of Contents, Summary, Numerical Results “Tables and Graphs”, Discussions, Conclusions, and References) [30%]
+10%Bonus: Deriving the equation of motion as given
Note: Consider how much more complex the model would have to be if could not neglect the pulley inertia. We could no longer take the cable tension to be the same on each side of the pulley, and we would need to write two additional equations of motion, one for the pulley rotation and one for its translation.