Write an adaptive Runge$-$Kutta program to simulate a pendulum system consisting of a bob of mass $m$ and a massless rod with rest length $L.$ The rod acts like a stiff spring with spring constant $k.$ Assume that the motion is in the $xy$ plane. Obtain plots of the motion for the values $m=0\mathrm{.}1kg,L=1\mathrm{.}0m,$ and spring constants in the range $k={10}^2\frac{N}{m}($rubber$)$ to $k={10}^6\frac{N}{m}($metal wire$).$ How does the average time step adopted by the algorithm vary with the spring constant? $[$Computer$]$