- For the periodic force signal shown below on the left: a. Is the force function f(t) an even or odd function? b. Draw the frequency spectrum (magnitude) of the force for the first three non-zero terms c. Draw the output frequency spectrum (magnitude, first three non-zero terms) if the input signal f(t) is connected to a first-order system (K=2, t=0.01sec). 3. 0.2 0.1 t (s) 0.02n

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Subject: Mechanical Measurements

**Transcription for Educational Website**

**Problem Statement:**

3. For the periodic force signal shown below on the left:

a. Is the force function \( f(t) \) an even or odd function?

b. Draw the frequency spectrum (magnitude) of the force for the first three non-zero terms.

c. Draw the output frequency spectrum (magnitude, first three non-zero terms) if the input signal \( f(t) \) is connected to a *first-order* system \( (K=2, \tau=0.01 \text{ sec}) \).

**Graph Description:**

The graph represents a periodic force signal \( f(t) \) plotted over time \( t \) in seconds. The vertical axis is labeled \( f(\text{kN}) \), ranging from 0 to 0.2 kN. The signal has a triangular waveform with a period marked as \( 0.02\pi \) seconds.

- The waveform starts at 0 kN and rises linearly to 0.2 kN, then decreases linearly to 0 kN, continues to -0.1 kN, and symmetrically mirrors this pattern returning to 0. Each complete cycle appears to have a peak amplitude of 0.2 kN and a trough amplitude of -0.1 kN.

**Additional Tasks:**
The tasks involve determining the nature of the function \( f(t) \) (even or odd), and constructing the frequency spectrum based on given system characteristics.
Transcribed Image Text:**Transcription for Educational Website** **Problem Statement:** 3. For the periodic force signal shown below on the left: a. Is the force function \( f(t) \) an even or odd function? b. Draw the frequency spectrum (magnitude) of the force for the first three non-zero terms. c. Draw the output frequency spectrum (magnitude, first three non-zero terms) if the input signal \( f(t) \) is connected to a *first-order* system \( (K=2, \tau=0.01 \text{ sec}) \). **Graph Description:** The graph represents a periodic force signal \( f(t) \) plotted over time \( t \) in seconds. The vertical axis is labeled \( f(\text{kN}) \), ranging from 0 to 0.2 kN. The signal has a triangular waveform with a period marked as \( 0.02\pi \) seconds. - The waveform starts at 0 kN and rises linearly to 0.2 kN, then decreases linearly to 0 kN, continues to -0.1 kN, and symmetrically mirrors this pattern returning to 0. Each complete cycle appears to have a peak amplitude of 0.2 kN and a trough amplitude of -0.1 kN. **Additional Tasks:** The tasks involve determining the nature of the function \( f(t) \) (even or odd), and constructing the frequency spectrum based on given system characteristics.
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