Problem 1. Consider three particles of mass m, M and m respectively, attached trough springs ideals of natural length L,

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Problem 1 Consider Three Particles Of Mass M M And M Respectively Attached Trough Springs Ideals Of Natural Length L 1 (63.94 KiB) Viewed 38 times

Problem 1. Consider three particles of mass m, M and m respectively, attached trough springs ideals of natural length L, and elastic constant k as shown in the figure. The particles they can only be moved about the x-axis. A) Write the lagrangian of the system. B) Find the equations of motion of the system. C) Find the equilibrium positions of the system and define the deviation variables qi. D) Suppose 4 = Aº exp(i9t) and show that the problema of finding the frequencies of this system reduces to a problema of eigenvalues and eigenvectors. E) Fin the frequencies of oscillation (921,923, ) F) Find the solutions or normal modes (Ay, A2, A3 for each frequency M m m k k