2. Consider the 2 DOF system below, with m = m, and m = 2m. The...

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2. Consider the 2 DOF system below, with m = m, and m = 2m. The system has the following initial conditions: x (0) = 5, x (0) = 2, (0) = 1, x (0) = 0. There are no frictional forces. a. Compute the normal modes of vibration of this system, for the case where: i. The position of mass 2 is defined as the absolute position of mass 2 (i.e. total displacement of mass 2 is x). ii. The position of mass 2 is defined relative to the position of mass 1 (i.e. the total displacement of mass 2 is x1 + x). iii. What do you notice about the symmetries of the mass and stiffness matrices for these two definitions of the generalized coordinates? b. Using modal superposition, compute the responses x(t) and x(t) and plot them using Matlab or Mathematica, for m = 1 and k = 4. 2k fm W X X2 mwww k m No friction 2. Consider the 2 DOF system below, with m = m, and m = 2m. The system has the following initial conditions: x (0) = 5, x (0) = 2, (0) = 1, x (0) = 0. There are no frictional forces. a. Compute the normal modes of vibration of this system, for the case where: i. The position of mass 2 is defined as the absolute position of mass 2 (i.e. total displacement of mass 2 is x). ii. The position of mass 2 is defined relative to the position of mass 1 (i.e. the total displacement of mass 2 is x1 + x). iii. What do you notice about the symmetries of the mass and stiffness matrices for these two definitions of the generalized coordinates? b. Using modal superposition, compute the responses x(t) and x(t) and plot them using Matlab or Mathematica, for m = 1 and k = 4. 2k fm W X X2 mwww k m No friction