II.1 Programming in MATLAB Getting Started Graphing

A2 – 3A L = 15 foot inextensible cord is tensioned by a spring havinga spring constant of k = 1000 pounds per foot and anunstretched length of a = 0.25 feet. A W = 20 pound weighthangs from point A, as shown. After some analysis, the tensionT in the cord (in pounds), the angle θ of the spring, and thestretch u of the spring were found to be related to each other bythe three equationsa = ( a + u) cosθ,W = ku sinθ,T = ku cosθ.It was determined from these equations that the angle θ of thespring is constrained by the equation0 = f(θ) = a – [a + W/(ksinθ)]cosθTo find the angle θ, plot f(θ) over the range of θ between 0 and90 ○ and locate from the graph where f(θ) = 0. Then, find thetension T in the cord and the stretch u in the spring.Answer: θ = 30.321 ○ , T = 34.2 pounds, u = 0.475 inches.A2 – 5A bridge is supported by cables that are suspended from acircular arch, as shown. The number of cables is 2n + 1. Thecables are tensioned to equal tensions T. After some analysis, inorder to support a 100 kilo-pound weight, it has beendetermined that the tension in the cables isT =1+2n∑Wsin kθ2k = 1 [cos kθ−1/(n + 1)] +sin2( kθ)πwhere θ = . Graph the tension T versus n for a range of2 ( n + 1)n between 1 and 10.Answer:T = 34.3, 23.1, 17.7, 14.4, 12.2 ,10.5, 9.27, 8.29, 7.50, 6.84 kilo - pounA2 – 4After analyzing the triangular truss given in problem A2 – 2, itwas determined that the unknown internal forces F AB and F ACand the unknown reactions at B and C, denoted by R Bx , R By , andR Cx , are related to each other by the five equations−FFFABAB− F− Fcosθ+ FAC= 0,sinθ= 500cosθ+ RBx= 0,sinθ+ RBy= 0,+ R = 0ABABACCxin which θ = 60 ○ . Placing the unknowns in the column vector x= [F AB F AC R Bx R By R Cx ] T , write these equations in matrix-vectorform as Ax = b. Then write a short program, find A -1 and then x= A -1 b.Answer: F AB = 577 lb, F AC = 289 lb, R Bx = -289 lb, R By = 500 lb,R Cx = 289 lb.10