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The input signal F(t) = 2 + sin 15.7t + sin 160t Newton is measured by a force measurement system. The system has a known wn = 100 rad/s, Z = 0.4, and K = 1 V/N. Write the expected form of the steady output signal in volts. Plot the resulting amplitude spectrum.

The input signal F(t) = 2 + sin 15.7t + sin 160t Newton is measured by a force measurement system. The system has a known wn = 100 rad/s, Z = 0.4, and K = 1 V/N. Write the expected form of the steady output signal in volts. Plot the resulting amplitude spectrum.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Problem Description The input signal \( F(t) = 2 + \sin 15.7t + \sin 160t \) Newton is measured by a force measurement system. The system has a known: - Natural frequency, \( \omega_n = 100 \, \text{rad/s} \), - Damping ratio, \( \zeta = 0.4 \), - Gain, \( K = 1 \, \text{V/N} \). ### Task 1. **Output Signal Formulation:** Write the expected form of the steady output signal in volts. 2. **Amplitude Spectrum Plot:** Plot the resulting amplitude spectrum. ### Solution Steps #### 1. Analyze the Input Signal: The given input signal consists of: - A constant term: \( 2 \) - Two sinusoidal components: \( \sin 15.7t \) and \( \sin 160t \) #### 2. System Response Characteristics: - The provided system characteristics \( \omega_n, \zeta, \text{and } K \) will affect each component of the input signal. - Calculate the response of the system to each input frequency. #### 3. Formulate Steady-State Output: - Calculate the steady-state output for each frequency component using transfer function analysis. - Combine the responses to form the total steady-state output signal in volts. #### 4. Amplitude Spectrum: - For each input frequency, calculate the amplitude of the corresponding component in the output. - Plot these amplitudes as a function of frequency to obtain the amplitude spectrum. This comprehensive approach will help you determine the expected output in volts and visualize its frequency components in the form of an amplitude spectrum.
Transcribed Image Text:### Problem Description The input signal \( F(t) = 2 + \sin 15.7t + \sin 160t \) Newton is measured by a force measurement system. The system has a known: - Natural frequency, \( \omega_n = 100 \, \text{rad/s} \), - Damping ratio, \( \zeta = 0.4 \), - Gain, \( K = 1 \, \text{V/N} \). ### Task 1. **Output Signal Formulation:** Write the expected form of the steady output signal in volts. 2. **Amplitude Spectrum Plot:** Plot the resulting amplitude spectrum. ### Solution Steps #### 1. Analyze the Input Signal: The given input signal consists of: - A constant term: \( 2 \) - Two sinusoidal components: \( \sin 15.7t \) and \( \sin 160t \) #### 2. System Response Characteristics: - The provided system characteristics \( \omega_n, \zeta, \text{and } K \) will affect each component of the input signal. - Calculate the response of the system to each input frequency. #### 3. Formulate Steady-State Output: - Calculate the steady-state output for each frequency component using transfer function analysis. - Combine the responses to form the total steady-state output signal in volts. #### 4. Amplitude Spectrum: - For each input frequency, calculate the amplitude of the corresponding component in the output. - Plot these amplitudes as a function of frequency to obtain the amplitude spectrum. This comprehensive approach will help you determine the expected output in volts and visualize its frequency components in the form of an amplitude spectrum.
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