Coding a Solution of the Duffing Oscillator

The Duffing Oscillator system is described in terms of a set of two simple coupled ODEs to solve. This solution can be obtained suffciently accurately via the Runge Kutta 4th order method.

The program to implement the numerical solution of the Duffing Oscillator can be derived from the Runge Kutta 4th order program to solve the mass on a spring problem.

Adapt this code according to the following steps

• Modify the RHS of the differential equation and the total energy according to the Duffing Oscillator equations

• Set initial conditions to $x_0 = 1.0$ and $v_0 = 0.0$ in set_initial_conditions()

• Define the model parameters as $\beta = 1$, $\alpha, \mu, A$ as zero, and $\omega = 1$ in define_model()

• Use $dt = 0.02$ and $t_{max} = 25.0$ in define_time_grid()

• Code a piece of logic to implement the recognition of three line arguments: -p, -i, and -t n

  They have the following functions:

  -p

  Print trajectory data. Default not to print.

  -i

  Read in the initial conditions $x_0$ and $v_0$ from <stdin> or cin until $EOF$ is reached.

  -t n

  To set $t_{max} = n 2 \pi / \omega$, $n$ times the period of the external driving term

• Implement the functionality of the three line arguments above.

  The -i option is implemented via an infinite $for(  ;  ;   )$ loop with a $if(     ) break;$ statement