PyXPlot

Examples - Pendulum

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The motion of a pendulum, as modelled exactly and in the small-angle approximation

Script

theta_approx(a,t) = a * sin(2*pi*t)
theta_exact (a,t) = 2*asin(sin(a/2)*jacobi_sn(2*pi*t,sin(a/2)))

set unit of angle degrees
set key below
set xlabel 'Time / $\sqrt{g/l}$'
set ylabel '$\theta$'
omega = unit(60*deg)
plot [0:4] theta_approx(omega,x) title 'Approximate solution', \
           theta_exact (omega,x) title 'Exact solution'
      

Notes

See Example 13 from the Users' Guide