MAE 316 Brookline College Crank Nicolson Solution Scheme Project

Consider a system with three masses and three springs in the ‘fixed-free’ configuration: that is, the masses are fixed at the top but free at the bottom. In addition to the spring forces, the system undergoes viscous dampening – imagine the masses are submerged in a viscous fluid that exerts a drag force. The force is proportional to the velocity of each mass and must be taken into consideration during the derivation of the governing equations. Write governing equations and a Crank Nicolson solution scheme – written in blockmatrix form, for the dynamics of the system. Write code : a function and a script, that solves the problem for the following masses and spring constants (with the top mass as mass 1):