Question

Five springs with different spring constants k, and unstretched lengths L, are attached to each other in series. The endpoint B is then displaced such that the distance between points A and B is L = 1.2 m. The four equations that govern the motions of the springs are shown below. Use Gauss elimination method to determine the positions xi,2, , x4 of the endpoints of the springs. The spring constants and the unstretched lengths of the springs are: Spring k (kN/m) 8 L(m) |0.18 4 12 0.19 15 10 |0.22 |0.26 0.15

please solve by hand, intermediate steps appreciated. thanks!

Answer 1

Four equa tions The euations are diP:ed o- 12. 18 -เว sai 19.78 62 o2 22

o11 1.60 19.72 16るSO l 62 19-78 6-IS O13 0a -8S 09 -18子! 。1668 66319 1o9 O12 a- 48

R3 → R3/1668 I09 o13 toR 109 0o 0-84 , 1-09 ις 350 iS1 39 -设 22 1-69-263 4100 一, ,8-78 oa 2 13a 34AS o 1 0-8ร์เ39-1659113900 -109 263 1700 134 50 3-659 1 จ. 139 340 R4 → Ru/ 1350 139 139 -IGS 13a 139 00 109 S9 500

I30 R니 1 39 o oo 3 るS00 O 8지 0303 131aS 19659 지- 1030 3 131 &S "Х. 3-659