Question

Determine the natural frequencies of the two-degree-of-freedom mechanical system of Figure P6.37

6.37 Determine the natural frequencies of the two-degree- of-freedom mechanical system of Figure P6.37. N N 2 x 10 3 x 10 10 2 kg 3 kg FIG. P6.37

Answer 1

지 Ня, Kan www mi m₂ M Kz Griven! Kia 2x105 Kg - 3x10 3x105 K3 = = 2X105 w/on N/m N/m m, a = 2 kg 3 kg mea For mass mi mm, E-K, - kg (1,– az ) e for mass m₂ + K3 P 2 - Kz ( 22 - x) M₂ X₂ 2. Let X, X, Sint and X = -X, w'sinwt H2 = X sinust -X Wasinut a

substituting Valves of Š, ,ja ,x, and X2 and @ in Equation 0 we get 3 - mW 2X, - - K,X-Kz (X, - *,) hy - m, w? X-Kg X3 - Kz (14-Y,) Reommarging Above equation, we get CA = 0 X , -K₂ X 2 ☺ , + Ky - m, wa). 6 -X, Kq + x2 ( Ky + Kz - Mewa)-0 Now Con conventing above Equation into Matuix fum Kitky - mw? -12 Xi 100 - Kz K₃ +K ₂ - mow? X 2 Now substituting Values in gives Equation -38905 SX105 - 2w2 XI -3x105 X2 4X105_302

detcuminant 5x105 - 202 Taking -3x105 -3x105 GROOS - 3W >>(se"-w7/906-302) – 9310" 9x10 20 > 20x1010 -23X105W wh+6w? - 981010 20 => 6we - 25x105 W² 10 MIXCO + ro Let wel -) 61² - 234105 1/X1010 co On sowing sowing we get, do = 327327.505 de = 56009.828 W2 l warde - 56009.828 W2=3273 23.505 wa 560091828 : ليبيا 327 323,505 Iwia s72.121 Mads ws 2 236.66 mad/e Ans: Ans.