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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply:

1 \cdot sin (wt) = sin (wt)

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

t^{4} e^{- 3 t} cos (2 t)

[(2^{3})^{3}]^{2}

\frac{3 y}{2 x}

(1 - 4 x)^{- 3}

50 e^{- 0.06 \cdot \frac{1}{12}}

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