Explanation Formula used: (1) L [ 1 ] = 1 s (2) L [ 1 s 2 ] = t Calculation: Consider the fourth order Laplace transform y ( 4 ) = k . Take Laplace transform on both side of the given differential equation and solve as follows. L ( y ( 4 ) ) = L ( k ) s 4 L ( y ) − s 3 y ( 0 ) − s 2 y ′ ( 0 ) − s y ″ ( 0 ) − y ‴ ( 0 ) = k s s 4 L ( y ) − a s 2 − b = k s [ Given y ′ ( 0 ) = a , y ‴ ( 0 ) = b ] s 4 L ( y ) = k s + a s 2 + b Simplify the above expression as follows. s 4 L ( y ) = k + a s 3 + b s s L ( y ) = k + a s 3 + b s s 5 L ( y ) = a s 2 + b s 4 + k s 5 Now, take inverse Laplace transform for the above obtained expression. y = L − 1 [ a s 2 ] + L − 1 [ b s 4 ] + L − 1 [ k s 5 ] y = a x + b 6 x 3 + k 24 x 4 [ from formula ( 2 ) ]

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 31.12, Problem 38E

To determine

To evaluate: The deflection y as a function of time x using Laplace transforms.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 31.12, Problem 37E

Chapter 31, Problem 1RE

Students have asked these similar questions

Table 15-21 shows the relative frequencies of the scores of a group of students on a philosophy quiz.Table 15-21 Score45678 Relative frequency7%11%19%24%39%

4. Dynamic regression (adapted from Q10.4 in Hyndman & Athanasopoulos) This exercise concerns aus_accommodation: the total quarterly takings from accommodation and the room occupancy level for hotels, motels, and guest houses in Australia, between January 1998 and June 2016. Total quarterly takings are in millions of Australian dollars. a. Perform inflation adjustment for Takings (using the CPI column), creating a new column in the tsibble called Adj Takings. b. For each state, fit a dynamic regression model of Adj Takings with seasonal dummy variables, a piecewise linear time trend with one knot at 2008 Q1, and ARIMA errors. c. What model was fitted for the state of Victoria? Does the time series exhibit constant seasonality? d. Check that the residuals of the model in c) look like white noise.

Q/ Solved by d'Alembert:- Utt = 5uxx u(x,o) - = sin X ut (X,0) = Sin 3X

Chapter 31 Solutions

Basic Technical Mathematics

Ch. 31.1 - Show that is a solution of . Is it the general...Ch. 31.1 - Prob. 1E Ch. 31.1 - In Exercises 1 and 2, show that the indicated...Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 4E Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 6E Ch. 31.1 - In Exercises 7–10, show that each function y =...Ch. 31.1 - Prob. 8E Ch. 31.1 - In Exercises 7–10, show that each function y =...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.