Question

the following problem is of a two-mass system. I have 2 questions

1. find the transfer function from input F2 to output x1

2. for the transfer function found, determine the sensitivity to variation in parameter B12

note: i already found the differential eqns of motion for t>0

Problem formulation Two masses are connected as shown in Fig. 1. Input forces Fi(t) and F.(t) act on masses m, and mg, respectively. The outputs are positions xi(t) and x2(t). Initial conditions are x 0), x0, x:(0) and x,0). mi m2 M kio B12 k20

Answer 1

Firstly, find the differential equations by applying laws of dynamic equilibrium. Subsequently, take the laplace transforms and express the equations in terms of X1(s) and F2(s). And finally, divide X1(s) by F2(s).
Sundaram DATE Consider mass Ama moyo SFx=0 miq = 8,2 M₂ + Kronq - F₂ - 1 Take Laplace Transform of a D? m 1s ²%₂C) -SX, CC) - & co] = Biz (sX, ) - X@] + Kxc Xos) - FS) 2289 alternator Consider Efnao mass , min, -kon,+B2 (rii B, 2 Cx - 4 Take Laplace Transform m, Lax's) -5%, -20] = KX, (s)? + B, 2 E (Sx, (s) - X, (o) - (sXcs) -x, co FCS)

KIPAGE NO. Sundaram DATE - X, (s) im, [su, co + 2 (0) - 8,2 X Otto - Big Sucs) - F, G) m, g2 - Ko-Bus Divide eq? (4 by eq 2 : TX,(s) am, Isa, cota (0) -B., [n, (0) + 2,(0) 7-8,5%(5) - Firs) Fa Cs) [m, s²-K, B,25] {mq [s x, (o) + a(co)] -B, z 22 (0) - 4 cs) [ma s² B. S = K20]} .