h2 h1 L2 G2 G1 L1 www www m2, k2 m1, k1 Fig 4a Fig 4b Figure Q4

Extracted text: h2 h1 L2 G2 G1 L1 www www m2, k2 m1, k1 Fig 4a Fig 4b Figure Q4


Extracted text: QUESTION 4 Two compound pendulums 01 and 02 are pivoted at a support and connected together through a horizontal spring of stiffness k as in Fig. 4a. The masses and radii of gyration of the pendulums about the centres of mass (G1 and G2) are m1 & m2 and kl & k2 respectively. The centres of mass are at distances hl and h2 respectively whilst the spring is distance I from the pivots as shown. The pendulums are set into motion by small displacements x1 and x2 opening up small angles 01 and 02 respectively as in Fig. 4b. Find the equations of motion of the two pendulums. 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.