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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 (GI 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 / 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. 4b. Find the equations of motion of the two pendulums. Also determine the natural frequencies of the vibration of the pendulums if ml =

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 (GI 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 / 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. 4b. Find the equations of motion of the two pendulums. Also determine the natural frequencies of the vibration of the pendulums if ml =

Refrigeration and Air Conditioning Technology (MindTap Course List)
Refrigeration and Air Conditioning Technology (MindTap Course List)
8th Edition
ISBN:9781305578296
Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Chapter26: Applications Of Refrigeration Systems
Section: Chapter Questions
Problem 2RQ: How are conditions maintained in open display cases when there are high shelves?
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h2 h1 L2 G2 G1 L1 www www m2, k2 m1, k1 Fig 4a Fig 4b Figure Q4
Transcribed Image Text:h2 h1 L2 G2 G1 L1 www www m2, k2 m1, k1 Fig 4a Fig 4b Figure Q4
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.
Transcribed Image 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.
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