A nonlinear second order ode was solved numerically using matlabs ode45. The user is advised to try different values for m and see the changes in the system. The following matlab project contains the source code and matlab examples used for duffing oscillator. You clicked a link that corresponds to this matlab command.
Use the poly function to obtain a polynomial from its roots. This same equation could also model the displacement and the velocity of a massspring system with a strange frictional force dissipating energy for large velocities and feeding energy for small ones. Zipped tar file for unixlinux 4k save the file vander. The poly function is the inverse of the roots function use the fzero function to find the roots of nonlinear equations. In particular, equation 1 serves after making several simplifying assumptions as a mathematical model of a generator on a triode for a tube with a cubic characteristic.
The source code and files included in this project. One can easily observe that for m0 the system becomes linear. Descargue como pdf, txt o lea en linea desde scribd. This behavior gives rise to selfsustained oscillations a stable limit cycle. For the love of physics walter lewin may 16, 2011 duration. The notation used here for representing derivatives of y with respect to t is y for a first derivative, y for a second derivative, and so on. Choose an ode solver ordinary differential equations. This matlab function, where r is a vector, returns the coefficients of the polynomial whose roots are the elements of r. Utilizing previous functions, show matlab results on following two options.
Numerical solution of differential equations lecture 6. In this program helps to find the phase portraits of the duffing oscillator as well as to save the data file from which we have to plot in present. You can find more information on how to use the applets on the following pages return here by hitting back. Solving odes in matlab to solve odes, one can use ode solvers in the matlab, e. Restricted second order information for the solution of optimal control problems using control vector parameterization. You can get help by typing help ode23tb in the matlab command window. To solve a second order ode, we must convert it by changes of variables to a system of first order odes. In your command window not the matlab window, cd to the directory where you saved the file, and enter the command. The first uses a relatively large time step of dt 0. Duffing oscillator in matlab download free open source. Mar 30, 2017 for the love of physics walter lewin may 16, 2011 duration.
103 369 103 775 18 1050 1265 1138 11 1550 1688 657 1588 295 337 1321 856 589 1574 991 346 1627 774 79 333 156 1371 1018 1208 646 446 526 458 833 284 337 843 541 1398 759 572 1209 1437 885