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

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 10:16

*Enlace a Spanish version

Summary:

This video presents the differential equation of a mass-spring system with friction $M\frac{d^{2}y}{d{t}^2}=-ky-b\frac{dy}{dt}$. Then, substituting the symbolic constant parameters for their numerical values obtains the general solution (with two constants of integration) using dsolve. This solution is analyzed, but, in order to better understand the ODE it is again solved, also with the same command, giving prescribed initial position and velocity values. The solution is graphically represented and animated, to understand the type of movement obtained (damped oscillations).

The dsolve command allows you to obtain an explicit expression of the solution formula, instead of just a set of points like the ode45 numerical simulations.

Additional simulations by varying parameters are covered in the video [masmusym2EN], and the animation Matlab code is detailed in the video [masmuAnimEN].

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