PHSX 220 Homework 13 D2L – Friday April 28 – 5:00 pm SHM and Pendula Problem 1: Shown below are 6 identical masses attached to springs and hung vertically. The masses are pulled down various distances and then released. The spring constant (k), spring sti ness, and the distance (d) that the mass is pulled down from its equilibrium position are given for each situation. The expression relating k and m to the angular frequency of the system is the same for both a horizontal and vertical spring-block system. Rank the situations based on the time it takes the mass to get from its maximum height to its minimum height from greatest to least. Problem 2: Shown below are systems containing a block resting on a frictionless surface and attached to the end of a spring. The springs are displaced to the right by a distance given in each gure and then released from rest. The blocks oscillate back and forth. The mass and spring constant are given for each system. Rank the cases based on the frequency of oscillation from greatest to least. Problem 3: Shown below are six masses hung on the ends of strings forming a pendulum. The masses have been pulled to the side and released so that they are swinging back and forth. For each pendulum the diagrams give the mass of the swinging object, the frequency of the swing, and how far, in terms of the angle from the vertical, that the masses were initially pulled to the side. Rank the six cases based on the length of the string from greatest to least. Problem 4: Shown below are four spring-cart systsems that consist of a spring connected to a cart. All systems are shown with the cart located at the equilibrium position. The cart is resting on a horizontal frictionless surface. If the cart is pulled to the right a small distance and released, the mass will oscillate back and forth. The amplitude of oscillation, mass of the cart and spring constants for the four cases are provided in the gure. Rank the cases shown based on their frequency of oscillation from greatest to least.

## PHSX 220 Homework 13 D2L – Friday April 28 – 5:00 pm SHM and Pendula Problem 1: Shown below are 6 identical masses attached to springs and hung vertically. The masses are pulled down various distances and then released. The spring constant (k), spring sti ness, and the distance (d) that the mass is pulled down from its equilibrium position are given for each situation. The expression relating k and m to the angular frequency of the system is the same for both a horizontal and vertical spring-block system. Rank the situations based on the time it takes the mass to get from its maximum height to its minimum height from greatest to least. Problem 2: Shown below are systems containing a block resting on a frictionless surface and attached to the end of a spring. The springs are displaced to the right by a distance given in each gure and then released from rest. The blocks oscillate back and forth. The mass and spring constant are given for each system. Rank the cases based on the frequency of oscillation from greatest to least. Problem 3: Shown below are six masses hung on the ends of strings forming a pendulum. The masses have been pulled to the side and released so that they are swinging back and forth. For each pendulum the diagrams give the mass of the swinging object, the frequency of the swing, and how far, in terms of the angle from the vertical, that the masses were initially pulled to the side. Rank the six cases based on the length of the string from greatest to least. Problem 4: Shown below are four spring-cart systsems that consist of a spring connected to a cart. All systems are shown with the cart located at the equilibrium position. The cart is resting on a horizontal frictionless surface. If the cart is pulled to the right a small distance and released, the mass will oscillate back and forth. The amplitude of oscillation, mass of the cart and spring constants for the four cases are provided in the gure. Rank the cases shown based on their frequency of oscillation from greatest to least.

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“The Terrible Transformation” for HY-135-701 Fall Semester 2017 Question 1 of 5 20.0 Points All of the following are true about unfree laborers in early Virginia except • A. they came from the English poor • B. they traded 4 to 7 years of labor in exchange for passage to Virginia • C. they received land at the end of their term • D. they were treated well by landowners Part 1 of 1 – Question 2 of 5 20.0 Points The first Africans to arrive in Jamestown were purchased as • A. slaves for life • B. indentured servants • C. indentured servants but with more years to serve than whites Question 3 of 5 20.0 Points The story of Anthony Johnson provides evidence that in the middle of the seventeenth century Africans in Virginia could • A. become free at the end of their term of service and purchase land • B. could become free but were prohibited from owning land • C. could never become free • D. could become free but must leave the colony Question 4 of 5 20.0 Points In 1665, all of the following happened except • A. Anthony Johnson left Virginia for Maryland • B. The Virginia colony took Johnson’s land • C. Johnson leased a plantation in Maryland • D. Johnson was forced into slavery Question 5 of 5 20.0 Points In September, 1739 a group of South Carolina slaves challenged white authority in • A. The Stono Rebellion • B. The Denmark Vesey rebellion • C. The Nat Turner rebellion • D. The Gabriel rebellion

## “The Terrible Transformation” for HY-135-701 Fall Semester 2017 Question 1 of 5 20.0 Points All of the following are true about unfree laborers in early Virginia except • A. they came from the English poor • B. they traded 4 to 7 years of labor in exchange for passage to Virginia • C. they received land at the end of their term • D. they were treated well by landowners Part 1 of 1 – Question 2 of 5 20.0 Points The first Africans to arrive in Jamestown were purchased as • A. slaves for life • B. indentured servants • C. indentured servants but with more years to serve than whites Question 3 of 5 20.0 Points The story of Anthony Johnson provides evidence that in the middle of the seventeenth century Africans in Virginia could • A. become free at the end of their term of service and purchase land • B. could become free but were prohibited from owning land • C. could never become free • D. could become free but must leave the colony Question 4 of 5 20.0 Points In 1665, all of the following happened except • A. Anthony Johnson left Virginia for Maryland • B. The Virginia colony took Johnson’s land • C. Johnson leased a plantation in Maryland • D. Johnson was forced into slavery Question 5 of 5 20.0 Points In September, 1739 a group of South Carolina slaves challenged white authority in • A. The Stono Rebellion • B. The Denmark Vesey rebellion • C. The Nat Turner rebellion • D. The Gabriel rebellion

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Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

## Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

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