Question

In Problems 3 - 24 fill in the blanks or answer true or false.

9. $\mathit{L}\left\{sin 2t\right\}$=-------

Short answer

$L\left\{\sin 2t\right\}=\frac{2}{s^2+4}$

Step-by-step solution

Consider the function

The function is,

$L\left\{\sin \left(2t\right)\right\}$

The standard formula is given as,

$L\left\{\sin at\right\}=\frac{a}{s^2+a^2}$

Compute the Laplace transform

Consider the function.

$\begin{array}{l}\mathrm{L}\left\{\sin \mathrm{at}\right\}\\ \mathrm{Here},\mathrm{a}=2\\ \mathrm{Substitute}\mathrm{the}\mathrm{value}\mathrm{and}\mathrm{find}\mathrm{the}\mathrm{Laplace}\mathrm{transform}.\\ \mathrm{L}\left\{\sin \left(2\mathrm{t}\right)\right\}=\frac{2}{{\mathrm{s}}^2+2^2}\\ \mathrm{Therefore},\mathrm{the}\mathrm{Laplace}\mathrm{transform}\mathrm{of}\mathrm{L}\left\{\sin \left(2\mathrm{t}\right)\right\}\mathrm{is},\\ \therefore \mathrm{L}\left\{\sin \left(2\mathrm{t}\right)\right\}=\frac{2}{{\mathrm{s}}^2+4}\end{array}$