Question

Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship for all springs/dampers. a. Draw representative free-body diagrams FBDS for the mechanical system. (5 Points) b. Apply Newton's laws to derive the mathematical model equations of the mechanical system. (5 Points) c. Obtain the transfer function for the mechanical system if the input is a(t) and the output is r1(t). (10 Points) Tw (t) 13 T. 12 b2 k4 k3 m2 k2 b3 k1 тi b1 Figure 2: Two-mass mechanical system subject to fluctuations r(t) at the right wall.

Answer 1

Hn6w ки в з нг , 210 ha Хусе - 1 ; с # M2 К- lurt enot & E,

☺ Fiz k(13-202) Ez = bz-d (3 kw) dt fz = K3 (22-243) Fu = r ²r2 tk (24,-4)+ b, d (0-12) + baduz dtz dt dt² dt Fs= Kz (2,-22) f6= bi d (11-06) olt Fq = duz at fo= m. d²e + K₂ (2, -42) + b, d(M, M2) aupy ot