Edwards Fernandez
06/08/2024 · Primary School
5) a) Sendo \( y=e^{-t} \cos 2 t \), verifique que \( \quad \frac{d^{2} y}{d t^{2}}+2 \frac{d y}{d t}+5 y=0 \) b) Seja \( y=\cos \omega t, \omega \) constante. Verifique que \( \quad \frac{d^{2} y}{d t^{2}}+\omega^{2} y=0 \)
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Para a parte a), substituindo as derivadas de \( y = e^{-t} \cos(2t) \) na equação \( \frac{d^{2} y}{d t^{2}} + 2 \frac{d y}{d t} + 5 y = 0 \), obtemos 0, verificando a equação. Para a parte b), substituindo as derivadas de \( y = \cos(\omega t) \) na equação \( \frac{d^{2} y}{d t^{2}} + \omega^{2} y = 0 \), também obtemos 0, verificando a equação.
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