Ee fisin

Multiplying both sides of this relation by sm.(jnx/i) and integrating over x from 0 to I yields cx3 />{

Applying the orthogonality property of the sine functions in the integrand indicates that

The same procedure can be applied to the initial velocity where

Again this relation can be multiplied by sm(jjtx/i) and integrated over the string length. The orthogonality property in this case yields

The zero initial conditions thus require that the generalized coordinates of the odd-indexed modes be written as

The constants C, of the particular integral can be determined by substitution of the generalized coordinate back into the generalized equations of motion. This yields

MiCi (wj - w2) sin (cot) —-sin(&>r ). (2.127)

With Eq. (2.48), M, = mi/2 and the third constant becomes 4 F

0 0

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