What is e^{-at}*sin(bt)u(t) ?

The solution to e^{-at}*sin(bt)u(t) is (tusin(tb))/(e^{at)}

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simplify e^{-at}*sin(bt)u(t)

simplify

e^{- a t} \cdot sin (b t) u (t)

\frac{t u sin ( t b )}{e ^{a t}}

Solution steps

e^{- a t} sin (b t) u (t)

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{a t}} t u sin (t b)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot sin ( b t ) u t}{e ^{a t}}

Multiply:

1 \cdot sin (b t) = sin (b t)

= \frac{t u sin ( t b )}{e ^{a t}}

(5.4 x 1 0^{- 4}) (9 x 1 0^{9})

e^{- 6} e^{17}

8.73 x 1 0^{- 8}

2.7 (101.53)^{- 0.265}

100000 \cdot e^{- 0.16 \cdot 1.5}

What is e^{-at}*sin(bt)u(t) ?
The solution to e^{-at}*sin(bt)u(t) is (tusin(tb))/(e^{at)}