# Consider the cube balanced on a cylinder as described in

Chapter 7, Problem 7.32

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QUESTION:

Consider the cube balanced on a cylinder as described in Example 4.7 (page 130). Assuming that 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 to before you differentiate to get Lagrange's equation. As usual, be careful in writing down the kinetic energy; this is Z (1111.12 + 162), where v is the speed of the CM and / 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.

QUESTION:

Consider the cube balanced on a cylinder as described in Example 4.7 (page 130). Assuming that 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 to before you differentiate to get Lagrange's equation. As usual, be careful in writing down the kinetic energy; this is Z (1111.12 + 162), where v is the speed of the CM and / 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.

Step 1 of 5

The Lagrangian  of a system is the function of generalized coordinates and generalized velocities. The mathematical expression of the Lagrangian equation of motion of a system is given by,

Here, , are the generalized coordinates and are the generalized velocities.

The Lagrangian of a system depends on kinetic energy  and potential energy .