The graph of f(t) is given in the figure. Represent f(t) using a combination of Heaviside step functions. Use h(t - a) for the Heaviside function shifted a units horizontally. f(t) = help (formulas) 3 4 Graph of y = f(t) t
The graph of f(t) is given in the figure. Represent f(t) using a combination of Heaviside step functions. Use h(t - a) for the Heaviside function shifted a units horizontally. f(t) = help (formulas) 3 4 Graph of y = f(t) t
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Heaviside Step Function Representation
The graph of \( f(t) \) is given in the figure. Represent \( f(t) \) using a combination of Heaviside step functions. Use \( h(t - a) \) for the Heaviside function shifted \( a \) units horizontally.
\[ f(t) = \]
[help (formulas)]
#### Graph Description:
The graph of \( f(t) \) is a piecewise function shown as follows:
- It remains at \( y = 0 \) for \( t < 1 \).
- At \( t = 1 \), the function value jumps to \( y = 1 \), increasing linearly.
- It continues to increase linearly until \( t = 2 \), reaching \( y = 4 \).
- From \( t = 2 \) to \( t = 3 \), \( y \) decreases linearly back to 1.
- Finally, at \( t = 4 \), the function value drops to \( y = 0 \) and remains there for \( t > 4 \).
#### Graph Coordinate Points:
- From \( t = 0 \) to \( t = 1 \), \( f(t) = 0 \)
- At \( t = 1 \), \( f(t) = 1 \)
- At \( t = 2 \), \( f(t) = 4 \)
- At \( t = 3 \), \( f(t) = 1 \)
- At \( t = 4 \), \( f(t) = 0 \)
Graphically:
```
5 -|
|
4 -| *
| / \
3 -| / \
| / \
2 -| / \
| / \
1 -|---/ \
| / \
0 -|__________________\
| 1 2 3 4 5
```
You are required to fill in \( f(t) \) in the text box using the proper Heaviside step functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb04829d0-4645-426e-bf1a-7ada40b0786f%2F1a72b673-d871-403b-8825-6f27bc27dabd%2Feke95po_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Heaviside Step Function Representation
The graph of \( f(t) \) is given in the figure. Represent \( f(t) \) using a combination of Heaviside step functions. Use \( h(t - a) \) for the Heaviside function shifted \( a \) units horizontally.
\[ f(t) = \]
[help (formulas)]
#### Graph Description:
The graph of \( f(t) \) is a piecewise function shown as follows:
- It remains at \( y = 0 \) for \( t < 1 \).
- At \( t = 1 \), the function value jumps to \( y = 1 \), increasing linearly.
- It continues to increase linearly until \( t = 2 \), reaching \( y = 4 \).
- From \( t = 2 \) to \( t = 3 \), \( y \) decreases linearly back to 1.
- Finally, at \( t = 4 \), the function value drops to \( y = 0 \) and remains there for \( t > 4 \).
#### Graph Coordinate Points:
- From \( t = 0 \) to \( t = 1 \), \( f(t) = 0 \)
- At \( t = 1 \), \( f(t) = 1 \)
- At \( t = 2 \), \( f(t) = 4 \)
- At \( t = 3 \), \( f(t) = 1 \)
- At \( t = 4 \), \( f(t) = 0 \)
Graphically:
```
5 -|
|
4 -| *
| / \
3 -| / \
| / \
2 -| / \
| / \
1 -|---/ \
| / \
0 -|__________________\
| 1 2 3 4 5
```
You are required to fill in \( f(t) \) in the text box using the proper Heaviside step functions.
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