The pendulum system in Figure 8.35 consists of a uniform thin rod of length l and a concentrated mass m at its tip. The friction at the pivot causes the system to be damped. When the angular displacement θ is not very small, the system is described by the nonlinear model

 

Assume, in consistent physical units, that ml² = 1.5 ,  = 6.8. Two sets of initial conditions

are to be considered: (1) θ(0 )  = 10°, ( 0)  = 0 , and (2) θ(0) = 20 °, (0) = 0. Using the RK4 method plot the two angular displacements θ₁ and θ₂ corresponding to the two sets of initial conditions versus 0 ≤ t ≤ 10 in the same graph. Angle measures must be converted to radians.