A Spring with A $16 - \mathrm { kg }$ Mass Has Natural Length

question 25

Multiple Choice

A spring with a $16 - \mathrm { kg }$ mass has natural length $0.8 \mathrm {~m}$ and is maintained stretched to a length of $1.2$ $\mathrm { m }$ by a force of $19.6 \mathrm {~N}$ . If the spring is compressed to a length of $0.4 \mathrm {~m}$ and then released with zero velocity, find the position $x ( t )$ of the mass at any time $t$ . Select the correct answer.

• A) \(x ( t ) = 0.8 \sin ( 1.75 t )\)
• B) \(x ( t ) = - 0.4 \cos ( 1.75 t )\)
• C) \(x ( t ) = - 0.4 e ^ { - 4 t } \cos ( 0.4 t )\)
• D) \(x ( t ) = - 0.4 e ^ { - 4 t } \cos ( 1.75 t )\)
• E) \(x ( t ) = - 0.4 \cos ( 1.75 t ) + 0.4 \sin ( 1.75 t )\)

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Definitions:

Reciprocal Method

An accounting technique used for allocating service department costs to operating departments by incorporating the mutual services provided among all service departments.

Support Departments

Units within an organization that provide essential services or assistance to other units rather than producing goods or services directly.

Cost Equations

Mathematical formulas used to calculate the total cost of producing goods or services, often incorporating variable and fixed costs.

Absorption Costing

A method of accounting that encompasses all costs associated with manufacturing (such as direct materials, direct labor, as well as both variable and fixed overhead expenses) in the pricing of a product.