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Unformatted text preview: 3 s + 12 = A ( s + 4) + B (3) Starting with the highest power of s , we find the value of A and B . Since the only term multiplying s on the right is A , we must have the following result: A = 3 Using this value for A , we can quickly find B . 3 s + 12 = 3( s + 4) + B (3) = 3 s + 12 + B (3) or B = Now we take the inverse transform to obtain our final result. f ( t ) = δ ( t ) + 3 e − 4 t cos(3 t ) u ( t ) N OTE : We multiply by u ( t ) as a reminder that we are uncertain of the value of f ( t ) for t < 0. Since δ ( t ) = 0 for t > 0, we need only multiply the second term by u ( t )....
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- Spring '12
- Division, Fraction, Elementary arithmetic, Multiplicative inverse