6) The following stress-strain points are generated for a titanium alloy for aerospace applications: (in MPa)(unitless)       Calculate Young’s modulus for this alloy. (Hint: think about whether you should use only some of the points or all of the points).

6) The following stress-strain points are generated for a titanium alloy for aerospace applications: (in MPa)(unitless)       Calculate Young’s modulus for this alloy. (Hint: think about whether you should use only some of the points or all of the points).

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A 15 cm long solenoid has 2000 turns of wire and is designed to cancel the earth’s magnetic field of near its center. How large must be the current through the wire? A. 0.01 mA B. 7.0 mA C. 14 mA + D. 21 mA E. 28 mA

A 15 cm long solenoid has 2000 turns of wire and is designed to cancel the earth’s magnetic field of near its center. How large must be the current through the wire? A. 0.01 mA B. 7.0 mA C. 14 mA + D. 21 mA E. 28 mA

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8) A heavy steel ball is attached to a light rod to make a pendulum. The pendulum begins at rest at instant A, as shown. The ball is then pulled to one side and held at rest. At instant B, the pendulum is released from rest. It swings down and passes its original height at instant C, as shown. The total mechanical energy of the pendulum is greatest at: a) Point B b) Point C c) Equal at both instants d) Since the mass of the ball and the height it is raised to before it is released is not given it is impossible to determine.

8) A heavy steel ball is attached to a light rod to make a pendulum. The pendulum begins at rest at instant A, as shown. The ball is then pulled to one side and held at rest. At instant B, the pendulum is released from rest. It swings down and passes its original height at instant C, as shown. The total mechanical energy of the pendulum is greatest at: a) Point B b) Point C c) Equal at both instants d) Since the mass of the ball and the height it is raised to before it is released is not given it is impossible to determine.

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Two piezometers ( to measure hydraulic head ) have been placed along the direction of flow in a confined aquifer that is 30.0 m thick. the piezometers are 300 m apart . The different in hydraulic head between the two is 1.5 m. the aqufer hydraulic conductivity (k) is 50 m/day , and the porosity (n) is 30% . Estimate the travel time for water to flow between the two piezometers.

Two piezometers ( to measure hydraulic head ) have been placed along the direction of flow in a confined aquifer that is 30.0 m thick. the piezometers are 300 m apart . The different in hydraulic head between the two is 1.5 m. the aqufer hydraulic conductivity (k) is 50 m/day , and the porosity (n) is 30% . Estimate the travel time for water to flow between the two piezometers.

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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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Question 3 An electric dipole moment, consists of two equal but opposite charges, + q and -q, separated by a distance, d. The magnitude of the dipole moment is p = qd and the electric dipole moment vector points from the negative towards the positive charge of the configuration. Consider a water molecule. The measured value of the electrical dipole moment of the water molecule is about . An ionized hydrogen atom happens to be 3.5 nanometers away from the center of the water molecule on the side away from its two hydrogen atoms and along the line defined by the molecule’s dipole moment. (Take the center of the water molecule to be the center of its oxygen atom. Also consider the water molecule to be essentially a small, nearly a point object). How large is the force on the ionized hydrogen atom and what is its direction? A. , attractive B. , repulsive C. , attractive D. , repulsive + E. , attractive

Question 3 An electric dipole moment, consists of two equal but opposite charges, + q and -q, separated by a distance, d. The magnitude of the dipole moment is p = qd and the electric dipole moment vector points from the negative towards the positive charge of the configuration. Consider a water molecule. The measured value of the electrical dipole moment of the water molecule is about . An ionized hydrogen atom happens to be 3.5 nanometers away from the center of the water molecule on the side away from its two hydrogen atoms and along the line defined by the molecule’s dipole moment. (Take the center of the water molecule to be the center of its oxygen atom. Also consider the water molecule to be essentially a small, nearly a point object). How large is the force on the ionized hydrogen atom and what is its direction? A. , attractive B. , repulsive C. , attractive D. , repulsive + E. , attractive

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