Problem 2 Consider the block of mass m, connected to a spring of spring constant k and placed on a inclined plane of angle a. Let , be the length of the spring at equili brium, and z be the elongation. The block oscillates and at the same time is rotating around origin O, in the plane of the inclined, by a variable angular velocity ở. 1. Calculate the degrees of freedom of the block 2. What is the kinetic energy of the block 3. What is the potential energy of the block 4. Write the Lagrangian function (don't derive the Euler Lagrange equa- tions) k reference plane m

Problem 2 Consider the block of mass m, connected to a spring of spring constant k and placed on a inclined plane of angle a. Let , be the length of the spring at equili brium, and z be the elongation. The block oscillates and at the same time is rotating around origin O, in the plane of the inclined, by a variable angular velocity ở. 1. Calculate the degrees of freedom of the block 2. What is the kinetic energy of the block 3. What is the potential energy of the block 4. Write the Lagrangian function (don't derive the Euler Lagrange equa- tions) k reference plane m

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

Question

Problem 2
Consider the blodk of mass m, connected to a spring of spring constant k and
placed on a inclined plane of angle a. Let l be the length of the spring at
equili brium, and a be the elongation. The block oscillates and at the same
time is rotating around origin O, in the plane of the inclined, by a variable
angular velocity .
1. Calculate the degrees of freedom of the block
2. What is the kinetic energy of the block
3. What is the potential energy of the block
4. Write the Lagrangian function (don't derive the Euler Lagrange equa
tions)
reference plane

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