Computational Physics - Department of Physics

266 8 Differential equations

-1

-0.5

0

0.5

1

0 10 20 30 40 50

θ

tˆ

Fig. 8.8Plot ofθas function of timeτwithQ= 2 ,ωˆ= 2 / 3 andAˆ= 0. 5. The mass of the pendulum is set equal
to 1 kg and its length to 1 m. The inital velocity isvˆ 0 = 0 andθ 0 = 0. 3.

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

vˆ

θ

Fig. 8.9Phase-space curve withQ= 2 ,ωˆ= 2 / 3 andAˆ= 0. 5. The mass of the pendulum is set equal to 1 kg
and its lengthl= 1 m.. The inital velocity isvˆ 0 = 0 andθ 0 = 0. 3.