Question

> DOF Free Vibration An o rweligible mass and length move in the vertical plane by spring and massen hux - 100 min the mass and length is pivoted at the middle point and 18 and masseo, shown. I - 123 m h Bite the Equations of Motion in Matrix Form ind the natural frequencies Find the mode shapes

Answer 1

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(AG2) 2m a) 2 -Kx-K(164) +2kxt K10 2t)- xcos (wtt) O(t)- Ocos (wt +) ct)=-wo cos (wtt ) Aster hearsnanging, put ct) ) in eans 04 4mwtRKLG Kl X.co ct)-wxcos frty) 2 (KA)6+RK-mu) x-o Kl wi2kl -mutzK Kl b) FA treguencies, IA1= 0. -umewini K K& -mwtzk 2 K-mw +2KL2

2 2 2 -lomuk+ ym+3) 2 umuu lomwik t 3K (Lompare with atbxtc=o) hoots, -btb2 yac 2a wlomkt iomk) ) 2 11 (ym) lo pikt mk 213 Sm 11 10 + N13 t 13 K 11 11 4 w2 2.1514 . 3486 m. 0.5104 1o 0 2.64 MZ. hadls o.5904 11 5 K w2 .4661 1.4667 100 c.55 nadls L-12in c). mode shapes -ymLu구3k -4(5)(2) (.4) +3(100) (v) V 1 -100 X17 7.2672 1 -1o0 X12 -Kl. 79.2612 1