The equation of the variable X is, X" + iX = 0 (2) The equation of the variable T is, T" +a²iT = 0 (3) The general solution of the equation (2) is, X (x) = c1 cos ax + c2 sin æx (4) At given condition x = 0 and x = L, X (0) = 0 and X (L) = 0 Substitute X (0) = 0 in equation (4), X (0) = c cos 0 +c2 sin o 0 = c +0 CI =0 Substitute c = 0 and X (L) = 0 in equation (4), X (L) = 0 + 2 sin al c2 sin al = 0 For non trivial solution cz # 0, sin al = 0 a = 4
The equation of the variable X is, X" + iX = 0 (2) The equation of the variable T is, T" +a²iT = 0 (3) The general solution of the equation (2) is, X (x) = c1 cos ax + c2 sin æx (4) At given condition x = 0 and x = L, X (0) = 0 and X (L) = 0 Substitute X (0) = 0 in equation (4), X (0) = c cos 0 +c2 sin o 0 = c +0 CI =0 Substitute c = 0 and X (L) = 0 in equation (4), X (L) = 0 + 2 sin al c2 sin al = 0 For non trivial solution cz # 0, sin al = 0 a = 4
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I dont understand why X(x)=c1cos(ax)+c2sin(ax). Can you please explain it to me?Thank you
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In Problems 7-10 a string is tied to the x -axis at x = 0 and at x = L and its initial displacement u ( x,.
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< Chapter 12.4, Problem 8E >
The equation of the variable X is,
X" + AX = 0 (2)
The equation of the variable T is,
T" + a²2T = 0 (3)
The general solution of the equation (2) is,
X(х) 3 с1 сos ax + c2 sin ax (4)
At given condition x = 0 and x = L,
X (0) = 0 and X (L) = 0
Substitute X (0) = 0 in equation (4),
X (0) = c1 cos 0 + c2 sin 0
0 = c1 + 0
ci = 0
Substitute c1 = 0 and X (L) = 0 in equation (4),
X (L) = 0 + c2 sin aL
c2 sin ¤L = 0
For non trivial solution c2 # 0,
sin aL = 0
a =
X GET 10 FREE QUESTIONS
Substitute the values of ci and a in equation (4),
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