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Represent the following waveforms by using the ramp r(t) and unit step u(t) functions.

Represent the following waveforms by using the ramp r(t) and unit step u(t) functions.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Represent the following waveforms by using the ramp r(t) and unit step u(t) functions.

### Waveform Analysis and Expression #### Graph Descriptions 1. **Graph (a): "Vee"** - **Description**: This graph shows a V-shaped waveform, starting from the origin (0, 0). From \(t = 0\) to \(t = 4\) seconds, the graph is a downward linear slope reaching \(-4\) on the \(x_1(t)\) axis at \(t = 4\) seconds. Then, it mirrors upwards to reach back to 0 at \(t = 6\) seconds. 2. **Graph (b): Mesa** - **Description**: This waveform is a "mesa" or flat-topped shape. It increases linearly from the origin, reaching \(x_2(t) = 4\) at \(t = 2\) seconds. It then remains constant until \(t = 4\) seconds. After that, it decreases linearly back to 0 at \(t = 6\) seconds. 3. **Graph (c): Sawtooth** - **Description**: This waveform is a sawtooth shape, rising steeply from the origin to \(x_3(t) = 4\) at \(t = 2\) seconds, quickly dropping to 0 by \(t = 3\) seconds, decreasing further to \(-4\) at \(t = 4\) seconds, and finally rising back to 0 at \(t = 6\) seconds. #### Expressions and Input Section - **(a) Provide the expression for waveform (a):** - Input field: \(x_1(t) = \_\_\_\_\_\) - **Submit Answer**: Tries 0/5 - **(b) Provide the expression for waveform (b):** - Input field: \(x_2(t) = \_\_\_\_\_\) - **Submit Answer**: Incorrect. Tries 1/3 - [Previous Tries] - **(c) Provide the expression for waveform (c):** - Input field: \(x_3(t) = \_\_\_\_\_\) - **Submit Answer**: Tries 0/3 Use the input fields to enter the mathematical expressions for the waveforms based on their graphical representation. The answer attempts are limited,
Transcribed Image Text:### Waveform Analysis and Expression #### Graph Descriptions 1. **Graph (a): "Vee"** - **Description**: This graph shows a V-shaped waveform, starting from the origin (0, 0). From \(t = 0\) to \(t = 4\) seconds, the graph is a downward linear slope reaching \(-4\) on the \(x_1(t)\) axis at \(t = 4\) seconds. Then, it mirrors upwards to reach back to 0 at \(t = 6\) seconds. 2. **Graph (b): Mesa** - **Description**: This waveform is a "mesa" or flat-topped shape. It increases linearly from the origin, reaching \(x_2(t) = 4\) at \(t = 2\) seconds. It then remains constant until \(t = 4\) seconds. After that, it decreases linearly back to 0 at \(t = 6\) seconds. 3. **Graph (c): Sawtooth** - **Description**: This waveform is a sawtooth shape, rising steeply from the origin to \(x_3(t) = 4\) at \(t = 2\) seconds, quickly dropping to 0 by \(t = 3\) seconds, decreasing further to \(-4\) at \(t = 4\) seconds, and finally rising back to 0 at \(t = 6\) seconds. #### Expressions and Input Section - **(a) Provide the expression for waveform (a):** - Input field: \(x_1(t) = \_\_\_\_\_\) - **Submit Answer**: Tries 0/5 - **(b) Provide the expression for waveform (b):** - Input field: \(x_2(t) = \_\_\_\_\_\) - **Submit Answer**: Incorrect. Tries 1/3 - [Previous Tries] - **(c) Provide the expression for waveform (c):** - Input field: \(x_3(t) = \_\_\_\_\_\) - **Submit Answer**: Tries 0/3 Use the input fields to enter the mathematical expressions for the waveforms based on their graphical representation. The answer attempts are limited,
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