Figure 5.3.6 shows th ree railway cars connected by buffer s compressed, but dis

Question

Figure 5.3.6 shows th ree railway cars connected by buffer s compressed, but disengage instead of stretching, With n3, kkk, k1 = k-0 in Eqs. (2) through (4), we get the system (17) 0 0 m 0 k -k RES.36The three cars of Example 2 which is equivalent to (18) with (19) that m m3, so that cc, then a brief computation gives (20) coefficient matrix A in Eq. (18). Hence the (21a) for the characteristic equation of the matrix A has eigenvalues corresponding to the natural frequencies (21b) of the physical system. For a numerical example, suppose that the first and third railway cars weigh 12 tons each, that the middle car weighs 8 tons, and that the spring constant is k 1.5 tons/ft, ie..k 3000 lb/ft. Then, using fps units with mass measured in slugs (a weight of 32 pounds has a mass of I slug), we have m1 = m3 = 750, m2 = 500, and 3000 3000 Hence the coefficient matrix A is -4 4 o A=| 6-12 6 0 44 (22) and the eigen alue-frequency pairs given by (2 la) a daib) are 0, ,= 0;

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