The Solution of the Eigenvalue Problem $y ^ { \prime \prime } + \lambda y = 0 , y ( 0 ) = 0 , y ( \pi ) = 0$

question 5

Multiple Choice

The solution of the eigenvalue problem $y ^ { \prime \prime } + \lambda y = 0 , y ( 0 ) = 0 , y ( \pi ) = 0$ is

• A) \(\lambda = n ^ { 2 } , y = \cos ( n x ) , n = 0,1,2 , \ldots\)
• B) \(\lambda = n ^ { 2 } , y = \sin ( n x ) , n = 1,2,3 , \ldots\)
• C) \(\lambda = n , y = \cos ( n x ) , n = 0,1,2 , \ldots\)
• D) \(\lambda = n , y = \sin ( n x ) , n = 1,2,3 , \ldots\)
• E) \(\lambda = n , y = \cos ( n x ) + \sin ( n x ) , n = 1,2,3 , \ldots\)

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Definitions:

Machine-Hours

Machine-Hours measure the amount of time machines are in operation during a certain period, often used for allocating machine-related expenses to products.

Activity Cost Pools

A method in cost accounting where costs are accumulated according to the activities that incur them.

Activity-Based Costing

A costing methodology that assigns costs to products and services based on the resources consumed in the production process.

Manufacturing Overhead

All indirect costs associated with manufacturing, such as utilities, maintenance, and salaries for supervisors, not directly tied to a specific product.