a) Use the Laplace transform on the second order ODE, y (t) + ay'(t) + by(t)...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
a) Use the Laplace transform on the second order ODE, y" (t) + ay'(t) + by(t) = q(t), y(0) = u, y'(0) = v, a, b e R, > to show that u(s + a) + v + L(q(t)) Y(s) := L(y(t)) = a? (s + )² + b – 4 b) Show that Y (s) in the previous point can be written as, s+ L(q(t)) 1 Z(s) = u- (s + )² + (b – 4) (s + )² + (b- (s + )² + (b – $)' and solve the problem when q(t) = 0. a) Use the Laplace transform on the second order ODE, y" (t) + ay'(t) + by(t) = q(t), y(0) = u, y'(0) = v, a, b e R, > to show that u(s + a) + v + L(q(t)) Y(s) := L(y(t)) = a? (s + )² + b – 4 b) Show that Y (s) in the previous point can be written as, s+ L(q(t)) 1 Z(s) = u- (s + )² + (b – 4) (s + )² + (b- (s + )² + (b – $)' and solve the problem when q(t) = 0.
Expert Answer:
Related Book For
Fundamentals of Electric Circuits
ISBN: 9780073301150
3rd edition
Authors: Matthew Sadiku, Charles Alexander
Posted Date:
Students also viewed these mathematics questions
-
Show that the solution of Can be written as Y = ebx (D1 cosh (b2 + c2 x + D2 sinh (b2 + c2 x) 0 dax 2
-
Show that van der Waals equation can be written as a cubic equation in the compressibility factor involving the reduced pressure and reduced temperature as (27 P 27 P2 512 T, (T+1) z2- - 1) z - Z3 ST...
-
Show that the secular equation (9.82) can be written as
-
Neutrons can be used in diffraction experiments to probe the lattice structure of crystalline solids. Since the neutron's wavelength needs to be on the order of the spacing between atoms in the...
-
Data pertaining to the current position of Lucroy Industries Inc. are as follows: Cash ................$ 800,000 Marketable securities.......... 550,000 Accounts and notes receivable (net) .......
-
A camera is listed for $599 less 30%, 20%, and 5%. (a) What is the net price? (b) What is the total amount of discount allowed? (c) What is the exact single rate of discount that was allowed?
-
An income statement for Cheries Pizza is included in the Working Papers. 1. Use the following information to calculate the breakeven point in sales dollars and unit sales for July. The August...
-
Strong Welding Equipment Company produces and sells welding equipment nationally and internationally. Following is information about two divisions. REQUIRED A. Calculate each divisions ROI. B....
-
Assume that 'SURFS' company imports wind surfs from United States to Turkey. The current price of a wind surf in United States is 2000 USD. The price of the same wind surf is 9500 TL in Turkey. a) If...
-
During the boom years of 2010-2014, ace mutual fund manager Diana Sauros produced the following percentage rates of return. Rates of return on the market are given for comparison. Calculate the...
-
An array is a collection of variables that are stored in orderin consecutive positions in the computer's memory. Depending on theprogramming language, the array index starts at 0 (C language) or...
-
a) The line y = 6x, for x 0, creates an acute angle, 0, with the x-axis. Determine the sine, cosine, and tangent ratios for 0. b) If the terminal arm of an angle, 0, lies on the line 4y+ 3x = 0, for...
-
Instruction Watch the TED talk again given by Dr. Billings and read the article published by Deloitte to answer the following questions. Support your claims with appropriate information presented in...
-
Andy's dream is to own and run a toy shop. He wants to open it up nine years from now, when he can save up enough money to get the inventory. He will set aside the $2,000 he has today in a mutual...
-
1. What ethical guidelines would you use in deciding how to respond to this client? Response:0 / 10002. How would you respond to Aaron? Why? Response. Aaron's current issues are related, in part, to...
-
3. An algebraic structure F consists of the set of integers between 0 and 5 inclusive (Z6), under the operation V, where a b = a + b + 3 (mod 6). a) Prove that F is a group? b) Evaluate the order of...
-
Transition Functions and Relations F2. Why is the (major) difference between function and relation interesting as related to classifying
-
Evaluate how many lines there are in a true rotational spectrum of CO molecules whose natural vibration frequency is w = 4.09 1014 s1 and moment of inertia I = 1.44 1039 g cm2.
-
A series RLC circuit has R = 80 , L = 240 mH, and C = 5 mF. If the input voltage is v(t) = 10 cos 2t find the currrent flowing through the circuit.
-
For the circuit in Fig. 7.91, find i0 for t > 0. 3 4 H 24 V 4 8
-
Determine the Fourier coefficients an and bn of the first three harmonic terms of the rectified cosine wave in Fig. 17.52. f(t) 10 -2 0 246 810
-
Use the health expenditure data of Section 16.6. The model is a probit regression of DMED, an indicator variable for positive health expenditures, against the 17 regressors listed in the second...
-
Suppose we obtain a kernel density estimate using the uniform kernel (see Table 9.1) with \(h=1\) and a sample of size \(N=100\). Suppose in fact the data \(x \sim \mathcal{N}[0,1]\). (a) Calculate...
-
Suppose we obtain a kernel regression estimate using a uniform kernel (see Table 9.1) with \(h=1\) and a sample of size \(N=100\). Suppose in fact the data \(x \sim \mathcal{N}[0,1]\) and the...
Study smarter with the SolutionInn App