# This example simulates two similar pendulums, coupled with a horizontal # spring. The motion is taken to be undamped. # # The plot shows the displacement of one of the pendulums, as a function of # time. It illustrates how energy (e.g. maximum displacement) oscillates # back and forth between the two. # You may run this example by doing: # # ode < coupled.ode | graph -T X -C # # or alternatively, to get a real-time plot, # # ode < coupled.ode | graph -T X -C -x 0 50 -y -0.6 0.6 # The equations are: # m*x1'' = - m*g*x1/l + k(x2 - x1) # m*x2'' = - m*g*x2/l - k(x2 - x1) xone' = vxone xtwo' = vxtwo vxone' = -g*xone/lone + k/mone * ( xtwo - xone) vxtwo' = -g*xtwo/ltwo - k/ltwo * ( xtwo - xone) k = 1 g = 9.8 # acceleration due to gravity lone = 5 ltwo = 5 mone = 1 mtwo = 1 xone = 0.0 xtwo = 0.3 vxone = 0 vxtwo = 0 print t, xone step 0,50
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