So steady state does not mean static doing the

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Unformatted text preview: . So steady state does not mean static. Doing the derivatives and substituting, ( j 0 ) Ae 2 Equivalently, ( j 0 ) A 2 2 F0 m e j F0 m 2 j (t ) F0 m e jt (6:30). (cos j sin ) . This is really two equations, one for the real part, and one for the imaginary part, which both need to be true at the same time. Separating them, 2 ( 2 0 ) A F0 m cos and j A F0 m j sin or A F0 m sin . Whenever we have equations like this sin 1 and of the tangent. In squaring and adding F0 2 2 2 2 these equations we have ( ) A ( ) cos and ( A) ( m ) sin , giving with sin and cos, we always think of the identity cos 2 22 0 2 2 2 F0 2 m 2 2 ( 2 0 ) 2 A2 ( ) 2 A2 ( F0 ) 2 (cos 2 sin 2 ) ( F0 ) 2 . Thus, (( 2 0 ) 2 ( ) 2 ) A2 ( F0 ) 2 . m m m F0 / m as the amplitude of driven, Dividing through and taking...
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This note was uploaded on 02/18/2011 for the course PHYS 320 taught by Professor Martinconner during the Spring '10 term at Open Uni..

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