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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 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
these equations we have ( ) A ( ) cos and ( A) ( m ) sin , giving with sin and cos, we always think of the identity cos
0 2 2 2 F0 2
( 2 0 ) 2 A2 ( ) 2 A2 ( F0 ) 2 (cos 2 sin 2 ) ( F0 ) 2 . Thus, (( 2 0 ) 2 ( ) 2 ) A2 ( F0 ) 2 .
F0 / m
as the amplitude of driven,
Dividing through and taking...
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