E 0₁ COOOOD k L m and wo. 2. Consider the two ideal pendulums connected by a massless spring, which move in the plane of the paper. When 0₁ = 02 = 0 the spring is in its relaxed state. (a) In terms of the pendulum lengths L, the spring constant k, the masses m and the generalized coordinates 0₁ and 02, write the Lagrangian in the small-angle limit. (If you wish, you can go directly to the small angle limit, rather than writing for arbitrary angles first, then taking the limit.) In the small-angle limit the form for L should not involve any sines or cosines. (b) Staying in the small-angle limit, write the equations of motion for ₁ and 02. Aside from 01, 02, 01 and 02, express your answer in terms of wp = √√/g/L and wo = √/k/m, instead of k, m, g and L. (c) Solve for the frequencies of the normal modes. Give your answer in terms of wp

E 0₁ COOOOD k L m and wo. 2. Consider the two ideal pendulums connected by a massless spring, which move in the plane of the paper. When 0₁ = 02 = 0 the spring is in its relaxed state. (a) In terms of the pendulum lengths L, the spring constant k, the masses m and the generalized coordinates 0₁ and 02, write the Lagrangian in the small-angle limit. (If you wish, you can go directly to the small angle limit, rather than writing for arbitrary angles first, then taking the limit.) In the small-angle limit the form for L should not involve any sines or cosines. (b) Staying in the small-angle limit, write the equations of motion for ₁ and 02. Aside from 01, 02, 01 and 02, express your answer in terms of wp = √√/g/L and wo = √/k/m, instead of k, m, g and L. (c) Solve for the frequencies of the normal modes. Give your answer in terms of wp