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F(s)=3s3−4s+13+2s2−4s+8F(s)=3s3−4s+13+2s2−4s+8 |
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F(s)=3s3−4s+13−2s2−4s+8F(s)=3s3−4s+13−2s2−4s+8 |
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F(s)=3s2−4s+9+2s2−4s+8F(s)=3s2−4s+9+2s2−4s+8 |
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F(s)=3s2−4s+4−2s2−4s+8F(s)=3s2−4s+4−2s2−4s+8 |
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F(s)=3s2−4s+13−2s2−4s+8 |
Utilizando essas duas propriedades, obtemos \(\mathcal{L}(e^{ct}sen(at))=\dfrac{a}{(s-c)^2+a^2}\). Portanto:
\(\mathcal{L}(f(t))=\mathcal{L}(e^{2t}sen(3t))-\mathcal{L}(e^{2t}sen(2t))=\dfrac{3}{(s-2)^2+9}-\dfrac{2}{(s-2)^2+4}=\dfrac{3(s^2-4s+8)-2(s^2-4s+13)}{(s^2-4s+13)(s^2-4s+8)}=\dfrac{s^2-4s-2}{(s^2-4s+13)(s^2-4s+8)}\)
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