Please also use the numbers. Below is a sample solution for other numbers for k and m... a) and b) must also get the numbers inserted (from k and m).

1) Lagrangian formalism: oscillations Lagrange's formalism for vibrational motion of two masses m, and m, connected by two fixed walls through springs in x-direction is given by x., and x 2 as the equilibrium positions of the two masses. and k , k,, k, are the spring constants. It holds that m, = 1/2m, = m, K 2 = 1/5 k, = 1/2 K = k a) Set up the Lagrange function. b) Formulate the motion equations. c) Calculate the eigenfrequencies of the coupled oscillations. K12 m2 WOW WW mi = my = m, k12 = =k2 - ski = k krafte : J. = - Rx ( xi->) Tze- Baz (mi-xxo) mix , = - 12z*2 + Raz (un-xx)= kuz kn=-y a) Lagrange: L= 9.mix. . Amx: - 14(xxxxx )- fun(max) X. . . (13x,-16x.) -) Ciganfrequent : xx= Arcos(we ), x,= Arcos(we1) ( - w + 17% - 16 # ) / 4) det ( m)- ( - worth ) - ( 10# ) =0 0 ( -Wink) = 1net W = ( 17: 16 )#