I don't why al=(2n-1)pi/2. Can you please explain it to me?Thank you 10:58 АМ Тhu May 6* 56%AAbartleby.com+M (108) - F G cascade yar...M (38,939) - s...y!YahooPM Trigonometri...Solve the bo...= bartlebyQ Search for textbooks, step-by-step explanatio...Ask an ExpertMath / Bundle: Differential Equations w... / Solve the boundary-value problem a 2 d 2 u d x 2 = d 2 u d t 2, 0 < x < L , t &...| Solve the boundary-value problem a 2 d 2 u d x 2 = d 2 u dt2,0 < x < L , t > 0 ...DIFFERENTIALEQUATIONS wthndary Value ProoBundle: Differential Equations wit...9th EditionDennis G. ZillPublisher: Cengage LearningDENNIS G ZILLFind 2ISBN: 9781337604901Chapter 12.7, Problem 6ETextbook ProblemSolve the boundary-value problema?dx20 < x < L, t> 0||dt2диu (0, t) = 0, Eª = Fo, t> 0dx [x=Lдии (х, 0) %3D 0, 0, 0 <х < L.|f=0The solution u(x, t) represents the longitudinal displacement of a vibrating elastic bar that isanchored at its left end and is subjected to a constant force of magnitude F, at its right end. SeeFigure 12.4.7 in Exercises 12.4. Eis a constant called the modulus of elasticity.Expert SolutionTo determineThe longitudinal displacement u (x, t) of a vibrating elastic bar such thata² *u = &u_u (0,1) = 0, u (x. 0) = 0, E = Fo and L = 0.dx Ix=Ldt Ix=LX GET 10 FREE QUESTIONSAnswer to Problem 6E 10:58 АМ Тhu May 6* 56%AAbartleby.com+M (108) - F G cascade yar...M (38,939) - s...y!YahooPM Trigonometri...Solve the bo...= bartleby Q Search for textbooks, step-by-step explanatio...Ask an ExpertMath / Bundle: Differential Equations w... / Solve the boundary-value problem a 2 d 2 u d x 2 = d 2 u d t 2 , 0 < x < L , t &...: Solve the boundary-value problem a 2 d 2 u d x 2= d 2 u dt 2,0 < x < L ,t > 0 ...X (x) = c8 sin (ax)(11)Differentiate the above equation with respect to x.X' (x)= ac6cos (ax)Substitute L for x in the above equation.XX' (L) == ac8cos (aL)ac8cos (aL) = 0(x' (L) = 0)(2n – 1) 5(2n – 1)aLa =Therefore, the Eigen values are as followsAn = an= ((2n – 1) )Substitute the value of a in equation (11).X (x) = cg sin ((2n – 1)TX2LThe above equation represents the Eigen functions where. n = 1, 2, 3, ....Substitute a? for 1 in equation (6).T" + a²a?T = 0The general solution of the above equation is as follows:T (t) = c9cos (aat) + c10sin (aat)(12)Differentiate the above equation with respect to t.T' (t)= -aac9 sin (aat) + aac10 cos (aat)Substitute 0 for t in the above equation.X GET 10 FREE QUESTIONS )(T' (0) = 0)

The value of the term inside the trigonometric functions can be expressed by using the variable n,…

Answered: I don't why al=(2n-1)pi/2. Can you…

I don't why al=(2n-1)pi/2. Can you please explain it to me

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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