Solving ordinary differential equations (ODE) with Matlab (dsolve): mass-spring forced response

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 13:41

*Enlace a Spanish version

Summary:

This video presents the solution of the mass-spring-damper ODE $Mÿ=-ky-bẏ+F(t)$ when subject to an input force with constant and sinusoidal components. The ‘free’ unforced response was discussed in video [masmusym1EN], which you might wish to watch prior to the one here.

It is verified that terms ”similar” to the input do appear: constants indicating the new equilibrium if the force has a constant component, and vibrations of the same frequency as the input (sinusoidal stationary regime); also, terms with components akin to those of the free response, with decay rate and fixed proper frequency of oscillations that do not depend on the characteristics of the input $F(t)$.

The result is plotted and animated, using the same code as explained in the video [masmuAnimEN] (animation details omitted here, please watch said video).

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.