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

question 70

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 $F ( t ) = 4 F _ { 0 } \cos ( \omega t )$ 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.

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

Recognize the homologous structures between male and female anatomy.

Comprehend the process and significance of ovulation in a woman's reproductive life.

Understand the composition and function of the innominate bone in human anatomy.

Define and describe the nature and function of hormones in the human body.

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Definitions:

Dopamine Production

The biochemical process leading to the creation of dopamine, a neurotransmitter vital for pleasure, motivation, and motor function in the brain.

Spinal Cord

A major part of the central nervous system which conducts sensory and motor nerve impulses to and from the brain.

Sensation

Processing of sensory stimuli that involves detection of nerve impulses by the cerebral cortex of the brain.

Voluntary Control

The ability to consciously control bodily movements, as opposed to involuntary movements which occur without conscious choice.