Question

2. The nonlinear pendulum is governed by the equations du g sin e dt dt L Solve using a) forward Euler and b) backward Euler for L = 9m, At 0.1s, vo = 0.6m s-1 and 0, 0. Integrate for 25s and plot v as a function of t. Comment on your results. Note that if a scheme is implicit, you may have to iterate 4o convergence at each time step. Use your own judgement on how best to do this.

Answer 1

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Soli Given's non-linear pendulum is governed by the Equation : d agsino dhe HL. - gsing e det +gsino = 0 de + 2Sin0 =0 multiply by with do on B-S. the last ) * 2 lade sino =0 en petz (4) cso) =0 se 14 6+{coso to sto) Mw; Multiply "me? "o.B-S:- [m2g2+mg Iwose] to take limits as oco to o=0 Saugular velocity} Oro toe. - So. Cos(0) = 1 to loso Jd mºo) +moge s dlose) = E = constant 6* {ml?o + mg 2 (uso -1).