Suppose a Spring Has Mass $M$ And Spring Constant $k$ And Let $\omega = \sqrt { k / M }$

question 104

Multiple Choice

Suppose a spring has mass $M$ and spring constant $k$ and let $\omega = \sqrt { k / M }$ . Suppose that the damping constant is so small that the damping force is negligible. If an external force $F ( t ) = 8 F _ { 0 } \cos ( \omega t )$ is applied (the applied frequency equals the natural frequency) , use the method of undetermined coefficients to find the equation that describes the motion of the mass.
Select the correct answer.

• A)
• \(x ( t ) = c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) + \frac { F _ { 0 } t ^ { - 2 } } { 2 M \omega } \sin ( \omega t )\)
• B)
• \(x ( t ) = c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) + \frac { F _ { 0 } e ^ { - \omega t } } { 2 M \omega }\)
• C)
• \(x ( t ) = c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) + \frac { 4 F _ { 0 } t } { M \omega } \sin ( \omega t )\)
• D)
• \(x ( t ) = \frac { F _ { 0 } t ^ { 2 } } { 2 M \omega } \cos ( \omega t )\)
• E)
• \(x ( t ) = \frac { F _ { 0 } t } { 2 M \omega } \left( c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) \right)\)

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Definitions:

AASB 141

An Australian Accounting Standards Board standard that concerns agriculture, detailing the accounting for agricultural activity including the transformation of biological assets (living plants and animals) into agricultural produce.

IAS 41

The International Accounting Standard that deals with the accounting for agriculture, including the recognition and measurement of biological assets.

Biological Assets

Living plants or animals that are held by an entity for the purpose of selling them, producing agricultural produce, or providing services.

Agricultural Produce

Products resulting from agricultural activities that have not been processed significantly, such as crops, livestock, and fisheries.