Solution Found!

Consider the cube balanced on a cylinder as described in

Chapter 7, Problem 7.32

(choose chapter or problem)

Get Unlimited Answers! Check out our subscriptions
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.

Not The Solution You Need? Search for Your Answer Here:

Questions & Answers

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.

ANSWER:

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 .

                                                                    

Add to cart


Study Tools You Might Need

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back