[Computer] The most general motion of the two carts of Section 11.2 is given by (11.21), with the constants A1, A2, 31, and 62 determined by the initial conditions. (a) Show that (11.21) can be rewritten as x(t) = (Bi cos wit + Ci sin wit) [ 1 1] + (B2 cos colt + C2 sin colt) [ 111 . This form is usually a little more convenient for matching to given initial conditions. (b) If the carts are released from rest at positions x1(0) = x2(0) = A, find the coefficients B1, B2, C1, and C2 and plot x1(t) and x2(t). Take A = col = 1 and 0 < t < 30 for your plots. (c) Same as part (b), except that x1(0) = A but x2(0) = 0

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