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Question Number 194887 by Mastermind last updated on 18/Jul/23

$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{Inverse}\mathrm{laplace}\mathrm{transform}\mathrm{of}$$$$\frac{\mathrm{S}+2}{{\mathrm{S}}^2+4\mathrm{S}+7}$$$$$$$$\mathrm{Urgent}!$$

Answered by Dwan last updated on 19/Jul/23

$$\frac{s+2}{s^2+4s+7}$$$$=\frac{s+2}{{(s+2)}^2+3}$$$$\mathcal{L}\left(cosat\right)=Re\left({\int }_0^{\mathrm{\infty }}{e}^{-st}{e}^{iat}dt\right)=Re\left(\frac{1}{s-ia}\right)$$$$=\frac{s}{s^2+a^2}$$$${\mathcal{L}}^{-1}\left(\frac{s+2}{{(s+2)}^2+3}\right)=cos\left(\sqrt{3}t\right)$$

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