A 2-Pound Weight Is Hung on a Spring and Stretches $x ( t )$

question 46

Multiple Choice

A 2-pound weight is hung on a spring and stretches it 1/2 foot. The mass spring system is then put into motion in a medium offering a damping force numerically equal to the velocity. If the mass is pulled down 4 inches from equilibrium and released, the initial value problem describing the position, $x ( t )$ , of the mass at time $t$ is

• A) \(x ^ { \prime \prime } - 16 x ^ { t } + 64 x = 0 , x ( 0 ) = 4 , x ^ { \prime } ( 0 ) = 0\)
• B) \(x ^ { \prime \prime } + 16 x ^ { t } + 64 x = 0 , x ( 0 ) = 4 , x ^ { \prime } ( 0 ) = 0\)
• C) \(x ^ { \prime \prime } - 16 x ^ { \prime } + 64 x = 0 , x ( 0 ) = 1 / 3 , x ^ { \prime } ( 0 ) = 0\)
• D) \(x ^ { \prime \prime } + 16 x ^ { \prime } + 64 x = 0 , x ( 0 ) = 1 / 3 , x ^ { \prime } ( 0 ) = 0\)
• E) \(x ^ { \prime \prime } + 64 x = 16 , x ( 0 ) = 1 / 3 , x ^ { \prime } ( 0 ) = 0\)

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Definitions:

Interquartile Range

The measure of variability which is the difference between the third quartile and the first quartile in a dataset, indicating the spread of the middle 50%.

Percentiles

Values or scores below which a given percentage of observations in a group of observations fall.

Decile

A statistical measure dividing a dataset into ten equal parts, each containing 10% of the data points.

Median

The middle value in a set of data, where half the numbers are above it and half are below, when the data is arranged in ascending order.