Problem_4.3 - Problem 4.3b Given2X=Cresin9 Show Satisfies...

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Unformatted text preview: Problem 4.3b) Given2X=Cresin9 Show: Satisfies Biharrnonic Equation. {52 /5r2 + l/r 5 /8r + 1/r2 52 /592} {52X/5r2 +1/r 5 X /5r +1/r2 52 X /592} Now, {52X/5r2 +1/r 5 X /5r +1/r2 52 X /592} = 0 +(C/r) a sine +Cr/r2[2(:os e w 9 sin 5] = = (2 C cos 6) / r Now perform operator on the left hand side of equation: = {52 {(2 C cos a) / r} /5rZ + 1/r 5 {(2 C cos 9) / r} /5r + 1/1»2 52%2 C cos 9) /r}/592}= +4CcosG/r3 —2CeosG/r3—2Ccos9/r3=0 Q.E.D. 5n = (C/r) a sine +(Cr/ r2)[ZCos e — 5 sin e] 0'99 2 0 0m = C/r [9 cos 9 + sin 9] ~— C/r [9 cos 9 + sin 6] = O ...
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