Integral of Laplace Transforms a. Find [latex]\mathcal{L}\left\{\frac{\sin \omega t}{t}\right\}[/latex]. b. Repeat in MATLAB.

a. Comparing with Equation 2.17, [latex]{\mathcal{L}}{\Bigg\{}{\frac{g(t){}}{t}\Bigg\}}=\int\limits_{s}^{\infty}\!G(\sigma)\,d\sigma[/latex] (2.17) we find [latex]g(t)=\sin \omega t[/latex] so that [latex]G(s)=\frac{\omega}{s^{2}+\omega^{2}}[/latex]. Consequently, [latex]\mathcal{L}\left\{\frac{\sin \omega t}{t}\right\}=\int\limits_{s}^{\infty} \frac{\omega}{\sigma^{2}+\omega^{2}} d \sigma=\int\limits_{s}^{\infty} \frac{1}{1+(\sigma / \omega)^{2}} \frac{d \sigma}{\omega}=\left[\tan ^{-1} \frac{\sigma}{\omega}\right]_{\sigma=s}^{\infty}=\frac{\pi}{2}-\tan ^{-1} \frac{s}{\omega}=\tan ^{-1} \frac{\omega}{s}[/latex]

Question 2.13: Integral of Laplace Transforms a. Find L {sinωt/t} t . b. Re...

Modeling and Analysis of Dynamic Systems

Integral of Laplace Transforms

a. Find $\mathcal{L}\left\{\frac{\sin \omega t}{t}\right\}$ .
b. Repeat in MATLAB.

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