Questions 1-7 please 1. In solving the beam equation, you determined that the general solution isx. Given that y'(1) = 3 determine q₁4_ = 9₁x²³² + 1/1 x .y =62. The particular solution xp for x' + 2x' = 4e¯³¹ is xp = q₂e-³12-313. In calculating the Laplace transform L{(1+2) H(1-5)} using the formulaL{f(t-a)H(t-a)} = eªsL{f(t)} on the Laplace sheet you calculated that the f(t)referred to in this formula isf(t) = **t +934. The Laplace transform5s² + 4s +6can be expressed as L{e [qssin(961) + 97cos(** t)]}5. The state-space representation for 2x" + 4x' + 5x = 10e' is11D-RJD+R-=6. Calculate the eigenvalue of the state-space coefficient matrix0 1-7a-2ausing the methodsdemonstrated in your lecture notes (Note that a is a positive constant, do not assume values for a). Ifyour eigenvalues are real and different, let ₁ be the smaller of the two eigenvalues when comparingtheir absolute values, for example, if your eigenvalues are -3 and -7, their absolute values are3 and 7 with 3 < 7 and 2₁ = -3. If your eigenvalues are a complex conjugate pair, let ₁ be theeigenvalue with the positive imaginary part.The eigenvalue you must keep is λ₁ =q₁1a + 912 a jNote that if is real valued that 912 = 07. The general solution of a non homogeneous state-space equation is given below. Use the initialconditions to determine the value of C₁.[x] = G₁ ² [2] + €₂6-²0 - [1]C₂e-2j)t-²5+ [_2 ;] + []given x(0) = 0, x'(0) = 2You calculated that C₁ = 913+914 jNote that if C₁ is a real number that 914 = 0.8. The specific solution of a state space equation is given below. Express the solution Qterms of sines and cosines using the Euler representation of the complex exponential.[i]=0.3je] -0.3je[¹]You calculated that Q=q1scos(t) +916sin(t)

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1. In solving the beam equation, you determined that the general solution is 1 y = 2x²9₁x²³+x. Given that_y'′(1) = 3 determine 9₁ 12 2. The particular solution xp for x' + 2x' = 4e-³¹ is xp = 9₂e-³t 3. In calculating the Laplace transform L{(t+2) H(1-5)} using the formula L{f(t-a)H(t-a)} = e¯ªsL{f(t)} on the Laplace sheet you calculated that the f(t) referred to in this formula is f(t) = **t +93 5 4. The Laplace transform can be expressed as L{e [qssin(961) + 97cos (** 1)]} s² + 4s +6

1. In solving the beam equation, you determined that the general solution is 1 y = 2x²9₁x²³+x. Given that_y'′(1) = 3 determine 9₁ 12 2. The particular solution xp for x' + 2x' = 4e-³¹ is xp = 9₂e-³t 3. In calculating the Laplace transform L{(t+2) H(1-5)} using the formula L{f(t-a)H(t-a)} = e¯ªsL{f(t)} on the Laplace sheet you calculated that the f(t) referred to in this formula is f(t) = t +93 5 4. The Laplace transform can be expressed as L{e [qssin(961) + 97cos ( 1)]} s² + 4s +6

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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