(3) 40%1 : : I• - E 0 0jrži 0 2 0||X2|+ Lo 0 1] Lëz. 2 -1 -1 -11X1 3 -1||X2 = -1 2 [X3 The above dynamics system has the

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3 40 1 I E 0 0jrzi 0 2 0 X2 Lo 0 1 Lez 2 1 1 11x1 3 1 X2 1 2 X3 The Above Dynamics System Has The 1 (145.88 KiB) Viewed 13 times

(3) 40%1 : : I• - E 0 0jrži 0 2 0||X2|+ Lo 0 1] Lëz. 2 -1 -1 -11X1 3 -1||X2 = -1 2 [X3 The above dynamics system has the following natural frequencies (in rad/sec) W1 = 0.4682, W2 = 1.5102, W3 = 1.7321 and mode shapes (y(i) = 1): = xin -- = - [o 2oe * = -1.zone] 1 x(1) = = 0.7808 1 X X(2) 1.2808 x(3) 0 (a) Decouple the above equations into three independent equations by substituting X1, X2, X3 with general displacements 91,92, and q3 as follows: [x1(t)] x2(t) = x(1)qı(t) + X(2)qz(t) + X(3)q3(t) [x3(t) b= (b) Given zero initial conditions, x1(0) = x2(0) = x30) = či (0) = *20) = x30) = 0, calculate (0 X1, X2, X3 in response to arbitrary fi and f3. Provide your solution with the forms containing convolutional integrals. = (c) Continue with (b), can you suppress the vibration of the highest natural frequency (W3 = 1.7321 rad/s) by choosing fi and f3? If so, what is the relation between fı and f3? (d) Continue with (b). Given fı = 0, f3 = 1 N for t > 0, and f3 = 0 for t < 0, calculate x1, x2 , X3.