Using Laplace Transform Methods, the Solution Of $y ^ { \prime \prime } + y = \delta ( t - \pi / 2 ) , y ( 0 ) = 1$

question 46

Multiple Choice

Using Laplace transform methods, the solution of $y ^ { \prime \prime } + y = \delta ( t - \pi / 2 ) , y ( 0 ) = 1$ , $y ^ { \prime } ( 0 ) = 0$ is

• A) \(y = \sin t + \sin ( t - \pi / 2 ) u ( t - \pi / 2 )\)
• B) \(y = \sin t - \cos ( t - \pi / 2 ) \boldsymbol { u } ( t - \pi / 2 )\)
• C) \(y = \cos t + \sin ( t - \pi / 2 ) u ( t - \pi / 2 )\)
• D) \(y = \cos t + \cos ( t - \pi / 2 ) \boldsymbol { u } ( t - \pi / 2 )\)
• E) \(y = \cos t - \sin ( t - \pi / 2 ) u ( t - \pi / 2 )\)

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Definitions:

Continental Hot Spot

A region on a continent where hot plumes of mantle material rise, causing volcanic activity and thermal phenomena.

Continental Rifting

The process by which a continent stretches and splits, possibly leading to the creation of new ocean basins.

Seafloor Spreading

A geological process in which new oceanic crust is formed at mid-ocean ridges and slowly moves away from the ridge.

Continental Hot Spot

A volcanic region thought to be fed by underlying mantle that is anomalously hot compared with the surrounding mantle, found in the interior of continental plates.