In the Previous Two Problems, If the Mass Is Set $x ( t )$

question 37

Multiple Choice

In the previous two problems, if the mass is set into motion in a medium that imparts a damping force numerically equal to 16 times the velocity, the correct differential equation for the position, $x ( t )$ , of the mass at a function of time, $t$ , is

• A) \(\frac { d ^ { 2 } x } { d t ^ { 2 } } + 4 \frac { d x } { d t } + x / 4 = 0\)
• B) \(\frac { d ^ { 2 } x } { d t ^ { 2 } } + 4 \frac { d x } { d t } + 2 x = 0\)
• C) \(\frac { d ^ { 2 } x } { d t ^ { 2 } } + 4 \frac { d x } { d t } + 4 x = 0\)
• D) \(\frac { d ^ { 2 } x } { d t ^ { 2 } } + 4 \frac { d x } { d t } + 8 x = 0\)
• E) \(\frac { d ^ { 2 } x } { d t ^ { 2 } } + 4 \frac { d x } { d t } + 32 x = 0\)

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Definitions:

Magnetic Resonance Imaging (MRI)

A non-invasive imaging technology that produces three-dimensional detailed anatomical images using strong magnetic fields and radio waves.

Transcranial Magnetic Stimulation (TMS)

A noninvasive method used to stimulate small regions of the brain using magnetic fields, often used in treating depression.

Spinal Cord

A long, thin, tubular structure made up of nervous tissue that extends from the medulla oblongata in the brain down to the lower back, acting as a major part of the central nervous system.

Brain

The organ located in the head of humans and other vertebrates that is the central hub for nervous system activity.