. . Problem 4. Consider three particles of mass m attached through ideal springs of natural length L. = 211 R/3. Particl

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Problem 4 Consider Three Particles Of Mass M Attached Through Ideal Springs Of Natural Length L 211 R 3 Particl 1 (119.73 KiB) Viewed 27 times

. . Problem 4. Consider three particles of mass m attached through ideal springs of natural length L. = 211 R/3. Particles can move only about a locus that is at a distance R from the origino f the coordinate system. Use as variables the three angles that describe the positions of the particles (01, 02, y 13) A) Show that the potential energy for this system is KIE (1 - ) - KAPE (03 – 0 – 3) * + (25 – 03 +0j? - 27 ) B) Write the lagrangian of the system. C) Find the equations of motion of the system. D) Suppose (p = A; exp(ist), and show that the problema of finding the frequencies of this system reduces to a problema of eigenvalues and eigenvectors. E) Find the frequencies of oscillation and the normal modes. 27 KRP 2 02 - 0 27 3 KR2 + 2 KR2 + 2 k კომნენ m m Fleeches 22024 oderobello Bagoon- m