Question

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

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

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

Short answer

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

Step-by-step solution

Given information.

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

Calculation.

Consider the given information.

Substitute 0.1 for $t$in the given function.

$$\begin{gathered} I\left(0.1\right)=0.8e^{-3\left(0.1\right)}\sin 10\left(0.1\right) \\ =0.8e^{-0.3}\sin 1 \\ =\text{0.49870} \end{gathered}$$

Substitute 0.5 for $t$in the given function.

$$\begin{gathered} I\left(0.5\right)=0.8e^{-3\left(0.5\right)}\sin 10\left(0.5\right) \\ =0.8e^{-1.3}\sin 5 \\ =-0.20906 \end{gathered}$$