Question

Consider the function 1. Write the function in terms of unit step functions. f(t) = (Notation: write u(t-c) for the unit step function u(t) with step at t = c.) 2. Find the Laplace transform of f(t) F(s) = \begin{cases} 0, & t < 1 \\ 3, & 1 \le t < 5 \\ (t-5)^2, & t \ge 5 \end{cases}

          Consider the function

1. Write the function in terms of unit step functions.
f(t) = 
(Notation: write u(t-c) for the unit step function u(t) with step at t = c.)

2. Find the Laplace transform of f(t)
F(s) = 
\begin{cases}
0, & t < 1 \\
3, & 1 \le t < 5 \\
(t-5)^2, & t \ge 5
\end{cases}

Consider the function

1. Write the function in terms of unit step functions.
f(t) =
(Notation: write u(t-c) for the unit step function u(t) with step at t = c.)

2. Find the Laplace transform of f(t)
F(s) =

0, t < 1

3, 1 ≤t < 5

(t-5)^2, t ≥5

Added by Spencer P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Joseph David

Step 1

Writing the function in terms of unit step functions: The function f(t) can be written as: f(t) = 1[u(t-1) - u(t-5)] - 5[u(t-5)] Here, u(t-c) represents the unit step function with a step at c. It is defined as: u(t-c) = 1, for t ≥ c u(t-c) = 0, for t < c So, Show more…

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Consider the function f(t) = 1[u(t-1) - u(t-5)] - 5[u(t-5)] 1. Write the function in terms of unit step functions f(t) = Notation write u(t-c) for the unit step function u with step at c. 2. Find the Laplace transform of f(t).