Question

3. (10 pts) The equations of motion of a mass and spring chain are given below in matrix form. 2m 0 3k -ki + -k 2k where m= 1 kg. The first (lowest) modal frequency and the second modal vector are given as am wum W1 2k k 10 radians/sec, and $2 = (-2). k (a) Determine the second modal frequency W2, i.e. the modal frequency associated with the modal vector 02. You should obtain a numerical answer with units. (b) Determine the first modal vector, P1, i.e. the modal vector associated with frequency w1. (You can obtain a numerical answer.)

Answer 1

* : رای 2 D 0.76 * *f3K 34 34 0 asej t 3 ke ty 2 kg = - if Tule - 4 y sin ut 22 = xq siy wt a seg = - 402 sinout x = -420² sinut .. (-2002 + 3R) - xs [-w2 tak 1 - kxa k xq

Amplitude teetin Frony 09- @l@ -w2fuk Ta R K -2002 +312 k2= . (-W² +22) C-QW²+ 3k) k2= 2004 trw²+ GR² 2004 - 7140² + 57250 7 £ 3k 161,29?- asso, (W, 12 72-3k f I wsp² = TK + 3/4 4 4 (10)2= AR 뇨 = 100 m ay TU! ut freq! We xj 고 x2 -2 bom eg © . 100 2 4 -20+ 300 -2002!+ 300 = - 206 . 500 2. Wp² Wa a Jaso IWp = 15.81 rudis $ 10, wa cielending to a is we = 15.81 reds.

뷔 Tu WI= 10 8uds & 2: = 100 Mr 2 몫 f00 -2(10)² + 30 0 100 2 100 외 1 X2 as Model vetter ut Wi= 10 rad, is 14 1.