Question

The displacement of point P on a clamped-clamped cable is shown in Figure (1), below, when the cable vibrates at its fourth mode shape. Point P is located at distance x m form the left hand supprot. The length of the cable is 100 m, its diameter is 15 mm, and the density of its material is 2700 kg/m3 The response of the cable is give by: lit W(x,t)sin(-x)cos(ct) Your are requested to: a. Determine the tension in the cable, T b. Determine the distance x c. Determine the first, second and third natrual frequencies of the cable d. On Figure (1), plot, schematically, the reponse of a point at 31/8 e. On Figure (2), plot, schematically, the response of a point at 1/2 1.5 E 0.5 0.2 0 Time (s) ).6 C-0.5 Figure (1): The response of point P when the cable vibrates in its fourth mode shape

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