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 *ml*^{2}* *= 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 θ_{1} and θ_{2} corresponding to the two sets of initial conditions versus 0 ≤ *t *≤ 10 in the same graph. Angle measures must be converted to radians.