What is e^{-at}cos(w_{0}t)u(t) ?

The solution to e^{-at}cos(w_{0}t)u(t) is (tucos(tw_{0}))/(e^{at)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify e^{-at}cos(w_{0}t)u(t)

simplify

e^{- a t} cos (w_{0} t) u (t)

\frac{t u cos ( t w _{0} )}{e ^{a t}}

Solution steps

e^{- a t} cos (w_{0} t) u (t)

Apply exponent rule:

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

= \frac{1}{e ^{a t}} t u cos (t w_{0})

Multiply fractions:

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

= \frac{1 \cdot cos ( w _{0} t ) u t}{e ^{a t}}

Multiply:

1 \cdot cos (w_{0} t) = cos (w_{0} t)

= \frac{t u cos ( t w _{0} )}{e ^{a t}}

e^{- 0.06116}

5^{8} \cdot e^{- 5}

(268 \cdot 1 0^{- 9}) (0.05112)

98.9 \cdot 1 0^{- 2}

What is e^{-at}cos(w_{0}t)u(t) ?
The solution to e^{-at}cos(w_{0}t)u(t) is (tucos(tw_{0}))/(e^{at)}