Harmonic Functions
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In our eReader you can find the full English version of the book. Read Harmonic Functions Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Harmonic Functions
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psinh ^ sinh^ -| 4 ^ . nx I a_ . ^nx is the required solution, for it reduces to i when y ^ b. See (7), Art. 6.
_y = O w.
hen X = o, y = o n x^l, dy It t = o, y =^/x ti t — o.
APPLICATIONS OF TRIGONOMETRIC SERIES. 39 {p) A harp-string is initially distorted into a given plane curve and then released ; find its motion.
The differential equation for the small transverse vibrations of a stretched elastic string is as stated in Art. i. Our conditions if we take one end of the string as origin are (...2) (3) (4) (5) Using the method of Art. 3, we easily get as particular solutions of (I) ■y = sin fix sin a fit, y = sin fix cos afit, y = cos fix sin afii, and y = cos fix cos a fit y = sin —J- cos— ^ satisfies (i), (2), (3), and (4), ,— - . mnx mnat k-^ y = ^a„, sin —1— cos — ^— , (o) where «'» = 7 fA^) sin ^7^ • ^^ (?) is our required solution ; for it reduces to/"(j^) when if = 0. See Art. 9.
Prob. 13. Three edges of a square sheet of tinfoil are kept at potential zero, and the fourth at potential unity ; at what potential is the centre of the sheet ?
What to read after Harmonic Functions?
You can find similar books in the "Read Also" column, or choose other free books by Byerly, William Elwood, B. 1849 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
psinh ^ sinh^ -| 4 ^ . nx I a_ . ^nx is the required solution, for it reduces to i when y ^ b. See (7), Art. 6.
_y = O w.
hen X = o, y = o n x^l, dy It t = o, y =^/x ti t — o.
APPLICATIONS OF TRIGONOMETRIC SERIES. 39 {p) A harp-string is initially distorted into a given plane curve and then released ; find its motion.
The differential equation for the small transverse vibrations of a stretched elastic string is as stated in Art. i. Our conditions if we take one end of the string as origin are (...2) (3) (4) (5) Using the method of Art. 3, we easily get as particular solutions of (I) ■y = sin fix sin a fit, y = sin fix cos afit, y = cos fix sin afii, and y = cos fix cos a fit y = sin —J- cos— ^ satisfies (i), (2), (3), and (4), ,— - . mnx mnat k-^ y = ^a„, sin —1— cos — ^— , (o) where «'» = 7 fA^) sin ^7^ • ^^ (?) is our required solution ; for it reduces to/"(j^) when if = 0. See Art. 9.
Prob. 13. Three edges of a square sheet of tinfoil are kept at potential zero, and the fourth at potential unity ; at what potential is the centre of the sheet ?
What to read after Harmonic Functions?
You can find similar books in the "Read Also" column, or choose other free books by Byerly, William Elwood, B. 1849 to read onlineMoreLess
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