A particle of mass 3m is suspended from the ceiling by a spring of force constant k. A second particle ofmass 2m is suspended from the first particle by a second identical spring. The rest lengths of both springsare lo. The particles can only move vertically. Gravity acts as usual in the vertical direction.www3mееееееее2mkk(a) How many degrees of freedom does the system have?(b) Choose appropriate generalised coordinates and write down the Lagrangian of the system in terms ofthem.(c) Write down the Euler-Lagrange equations (by this I mean the explicit equations, so do perform thederivatives of the Lagrangian).(d) Find the equilibrium position of the particles. Is it stable?Note: Remember our general three-step procedure for solving problems:1. Find adequate generalised coordinates {9;} to describe the motion of the system. The number ofthese coordinates, M, is the number of degrees of freedom of the system. I will collect them in anM-dimensional vector, which I call q.2. Re-express the kinetic energy T = ₁ m/2 in terms of the generalised coordinates and momentaq and q (here n is the number of particles in the system).d ƏLdt əq3. Write the Lagrangian L(q, q) = T(q, 4) - V(q). There will be one Lagrange equation for each gener-alised coordinate q; you have, corresponding to each degree of freedom. These equations are=ƏLƏq

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