Question

The equation for the unforced, damped pendulum is 2 d0 -mg sin ml 2 dt which, calling 0 by x, can be written as a pair of first order ODE's dx 2 dt For Quiz 9, please submit the phase plane for equations (1) with the values -1,e1 in the ranges -8 < x < 8,-3< y < 3. 0 In particular, draw in the three trajectories passing through the points Submit the same diagrams for the undamped case e 0, a)i 1

Answer 1

e d pen dulom is Thc cquationFR the untRed domp ml d e dt dr linealing the System at OOE atequiibliuim Ponl (n)

value 04 2 ス a saddle Point saddie PonH The com( Answer i's