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

question 33

Multiple Choice

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

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

---

Definitions:

Present Value

The contemporary valuation of future financial inflows or a lump sum, adjusted for a specific rate of return.

Rate of Return

A measure of the gain or loss on an investment over a specified period, expressed as a percentage of the investment's initial cost.

Net Working Capital

Net Working Capital is a financial metric that calculates the difference between a company's current assets and its current liabilities, indicating the company’s short-term financial health.

Project Analysis

Project analysis involves evaluating the feasibility, viability, and expected return of a project prior to making a commitment of resources.