See attached file: 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...

See attached file: 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):   m1 m2 m3   =   200 30 100     c1 c2 c3   =   50 100 20   (1) with initial conditions u0 =   −1 1 1   v0 =   0 0 0   (2) Run a case first without dampening – that is, with all dampening coefficients equal to zero. Then run two additional cases with   b1 b2 b3   =   50 0 0   (3) and   b1 b2 b3   =   50 0 10   (4)


MAE 316 Mini Project 2 Full Assignment October 28, 2020 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 block- matrix 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):m1m2 m3  = 20030 100  c1c2 c3  =  50100 20  (1) with initial conditions u0 = −11 1  v0 = 00 0  (2) Run a case first without dampening – that is, with all dampening coefficients equal to zero. Then run two additional cases withb1b2 b3  = 500 0  (3) and b1b2 b3  = 500 10  (4) 1