{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Solving for the transform of the solution

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: g ceases, 6. Taking the Laplace transform of both sides of the ODE, we obtain . Applying the initial conditions, . Solving for the transform, . Using partial fractions, ________________________________________________________________________ page 288 —————————————————————————— CHAPTER 6. —— and Taking the inverse transform. term-by-term, the solution of the IVP is Due to the initial conditions, the response has a transient overshoot, followed by an exponential convergence to a steady value of . 7. Taking the Laplace transform of both sides of the ODE, we obtain . Applying the initial conditions, ________________________________________________________________________ page 289 —————————————————————————— CHAPTER 6. —— . Solving for the transform, . Using partial fractions, . Hence . Taking the inverse transform, the solution of the IVP is Due to initial conditions, the solution temporarily oscillates about forcing is applied, the response is a steady oscillation about . . After the ________________________________________________________________________ page 290 —————————————————————————— CHAPTER 6. —— 9. Let be the forcing function on the right-hand-side. Taking the Laplace transform of both sides of the ODE, we obtain . Applying the initial conditions, . The forcing function can be written as with Laplace transform . Solving for the transform, . Using partial fractions, Taking the inverse transform, and using Theorem , the solution of the IVP is ________________________________________________________________________ page 291 —————————————————————————— CHAPTER 6. —— The solution increases, in response to the ramp input, and thereafter oscillates about a mean value of . 11. Taking the Laplace transform of both sides of the ODE, we obtain . Applying the initial conditions, . Solving for the transform, . Using partial fractions, Taking the inverse transform, and applying Theorem , . ________________________________________________________________________ page 292 —————————————————————————— CHAPTER 6. —— Since there is no damping term, the solution responds immediately to the forcing input. There is a temporary oscillation about 12. Taking the Laplace transform of the ODE, we obtain Applying the initial conditions, . Solving for the transform of the solution, . Using partial fractions, It follows that ________________________________________________________________________ page 293 —————————————————————————— CHAPTER 6. —— Based on Theorem , the solution of the IVP is . The solution increases without bound, exponentially. 13. Taking the Laplace transform of the ODE, we obtain Applying the initial conditions, . Solving for the transform of the solution, ________________________________________________________________________ page 294 —————————————————————————— CHAPTER 6. —— . Using partial fractions, It follows that Based on Theorem , the solution of the IVP is . That is, . ________________________________________________________________________ page 295 —————————————————————————...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online