Two blocks of masses m1=m and m2=2m are connected between and to the supports by three linear springs of spring constants of k, k, and 2k, respectively, as shown. The blocks are subjected to a pair of forces and move on a smooth horizontal surface along a straight line. Assume that the motion starts from rest. Take m=2kg and k=5N/m.

known information:

eigenvalues: w1^2= (10+(sqrt4100))/16, w2^2=(10-(sqrt4100))/16

natural frequency: w1= 2.15 rad/s, w2= DNE

lambda= matrix [4.627,0;0,-3.377]

mode shapes: X1= [1;0.1492]; X2=[0.2984;1]

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1. Find the modal matrix and the generalized mass and stiffness coefficients of the system.

2. assume that 

Find and plot the system responses x1(t) and x2(t).
 

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m k www-f x (t) f(t) k NNN 2m x (t) (t) 2k ANN m k www-f x (t) f(t) k NNN 2m x (t) (t) 2k ANN