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Q81.

Expert-verifiedFound in: Page 418

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**After the switch is closed in the circuit shown, the current $t$ seconds later is $I\left(t\right)=0.8{e}^{-3t}\mathrm{sin}10t$. Find the current at the times,**

**(a). $t=0.1\text{s}$**

**(b). $t=0.5\text{s}$**

The value of the function at $t=0.1$ and $t=0.5$is $0.49870$ and $-0.20906$.

The given function is $I\left(t\right)=0.8{e}^{-3t}\mathrm{sin}10t$.

Consider the given information.

Substitute 0.1 for $t$ in the given function.

$I\left(0.1\right)=0.8{e}^{-3\left(0.1\right)}\mathrm{sin}10\left(0.1\right)\phantom{\rule{0ex}{0ex}}=0.8{e}^{-0.3}\mathrm{sin}1\phantom{\rule{0ex}{0ex}}=\text{0.49870}$

Substitute 0.5 for $t$ in the given function.

$I\left(0.5\right)=0.8{e}^{-3\left(0.5\right)}\mathrm{sin}10\left(0.5\right)\phantom{\rule{0ex}{0ex}}=0.8{e}^{-1.3}\mathrm{sin}5\phantom{\rule{0ex}{0ex}}=-0.20906$

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