Question

k = 1.5

Question 2: Hanging Cable It can be shown that the curve y(x) of an inextensible flexible homogeneous cable hanging between two fixed points is obtained by solving the following equation: 22 / 1+1 =k, dr where the constant k depends on the weight. This curve is called a "catenary' ("chain' in Latin). Find and plot y(x), assuming a given value for k and those fixed points are (-1,0) and (1,0) in a vertical xy-plane, using the 4th order Runge-Kutta method with a step of 0.025. N.B. you should use a reasonable estimate for the initial slope and modify the spreadsheet until the solution is correct i.e. the slope at the midpoint is zero.

Have been asked to use MATLAB to plot

Answer 1

ANSWER:- Given slope equation pone and z!= K JI+22 2' - 015 Vi+22 de VI-ZA Vanables are seperated ,z appears on the right side and a on left Integrate the left side and x on lepe right side o relation to z Jox la de la 2+2 e antz Sn5'2 - 3 (THC) z = sinh ( Catc,)) 8': sinh (8 (11) 4 : goh (8 (zic). : c: sinh (đ (zic ))dx Again the variables seperated , x appears on right side and y and left side integral both the sales Jdy - lamb ( 1 (etc.)) dx

yo cooh (9 (4101)) +62 --> 0) peut 46-1).0 and ye1) - 0 in 0 ann le got cosh ( 311-1)+8.10 of cash (13 (1401)) +6-0 if cosh (3 (1-1)) + = cosh (3 (1461)) +62 put 9=0 then, cash (10-11)+c=0 substiteste in can then, Ty. if cosh fr - f. cosh (8) t Vertical xy-plane By using Range - Koelen method uth order 4841* Yi + (QIR 1+Q2k2 +Q3k3 +Quky ) WYpH = Y; + $ (kı +2kg +2 kg+x4) 1 Kis f(x1+4;) Korf(+dh, yi ti oh) Rg : + (21 b . Yi+ olkeb) K4 = + (th, ynt kigh)

By using this method step of 0.025 - h= 0.025 RH 4th model: đi 100% - 9ị (K+ Ky+ 2kg ) * 0-085 here -KIEL KQ = 1.3 kg = 0.6 k4 - 0.8 put values *I cosh ga- . cooh (3) te (cosh (15)1 – cash 15) (cosh 01:52 - cosh 15 )+ (149x13 + 2x0-6+0.8) XO-O8G 4,40.025 (cash 152 – cos h 15 ) +0.023 cosh 1051 - cosh A5 +0:093 cosh 75 2 - x 2.352 +0-083 : cosh 1.5% - 3.528+0.003 cosh1:52 – 8.551 .. vertical ay-plane Hi +0.095 coch 152 – 3:55) *** - Thanking you