[10] (4) Consider the cube balanced on a cylinder as shown in Figure. If b<r, use the Lagrangian approach to find the angular frequency of small oscillations about the top. [The simplest procedure is to make the small angle approximations cos = 1-0²/2 and sin 00 to before you differentiate to get Lagrange's equation.] Be careful in writing down the kinetic energy; this is ½ (my²+10²), where v is the speed of the CM and I is the moment of inertia about the CM (2mb²/3). The safe way to find v is to write down the coordinates of the CM and then differentiate. [5] (4.a) Write down the Lagrangian in terms of 0, 8, and the other constants: r, b, m and g. [3] (4.b) Find the Lagrange equation of motion. [2] (4.c) Find the angular frequency @ of small oscillations for b<r. CM of the block C 0/r D B h