h2h1L2G2G1L1wwwwwwm2, k2m1, k1Fig 4aFig 4bFigure Q4 QUESTION 4Two compound pendulums 01 and 02 are pivoted at a support and connected together througha horizontal spring of stiffness k as in Fig. 4a. The masses and radii of gyration of thependulums about the centres of mass (G1 and G2) are m1 & m2 and kl & k2 respectively. Thecentres of mass are at distances hl and h2 respectively whilst the spring is distance I from thepivots as shown. The pendulums are set into motion by small displacements x1 and x2 openingup small angles 01 and 02 respectively as in Fig. 4b. Find the equations of motion of the twopendulums. Also determine the natural frequencies of the vibration of the pendulums if m1 =7.5 kg, m2. = 6 kg, kl = 0.433 m, k2. = 0.3464 m, L1 = 1.5 m, L2. = 1.2 m, h1 = 0.75 m, h2. =0.6 m, 1= 0.9 m, and k = 1600 N/m.

Given Datam1=7.5kgm2=6kgk1=0.433mk2=0.3464mL1=1.5mL2=1.2mh1=0.75mh2=0.6ml=0.9mk=1600N/m

Answered: Two compound pendulums 01 and 02 are…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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h2 L2 G2 G1 L1 www x2 www m2, k2 02 m1, k1 Fig Qa Fig Qb Two compound pendulums of lengths L1 and L2 are pivoted at a support and connected together through a horizontal spring of stiffness k as in Fig Qa. The masses and radii of gyration of the pendulums about the centres of mass (G1 and G2) are m1 & m2 and k1 & k2 respectively. The centres of mass are at distances hl and h2 respectively whilst the spring is distance 1 from the pivots as shown. The pendulums are set into motion by small displacements xl and x2 opening up small angles 01 and 02 respectively as in Fig Qb. 4.1 Find the equations of motion of the two pendulums. 4.2 Also determine the natural frequencies of the vibration of the pendulums if mı = 10 kg, m2 = 8 kg, kı = 0.433 m, k2. = 0.3464 m, L1 = 1.2 m, L2. = 1.0 m, hi = 0.6 m, h2. = 0.5 m, 1= 0.8 m, and k = 2000 N/m.
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