Answer:Properties of ROC of Laplace Transform If x(t) is absolutely integral and it is of finite duration, then ROC is entire s-plane. If x(t) is a right sided sequence then ROC : Re{s} > o. If x(t) is a left sided sequence then ROC : Re{s} < o. If x(t) is a two sided sequence then ROC is the combination of two regions.
Explanation:
Given function is xt= detal(t)+u(t)We know that Laplace transform of `u(t)` is `1/s` and Laplace transform of `delta(t)` is 1.To find the Laplace transform of xt we will apply the linearity property of Laplace transform.Laplace transform of xt=L{delta(t)} + L{u(t)}Using Laplace transform of delta(t) and u(t),
we get; Laplace transform of xt = 1 + 1/sSo the Laplace transform of xt is `1 + 1/s`.The region of convergence (ROC) is given by Re[s] > -a where ‘a’ is a constant.The pole zero plot is given below:
Explanation:The region of convergence (ROC) is given by Re[s] > -a where ‘a’ is a constant.The pole zero plot is given below:Therefore, the Laplace transform and the associated region of convergence and pole zero plot for xt = delta(t) + u(t) are given as follows;
Laplace Transform = 1 + 1/sRegion of convergence: Re[s] > 0Pole-zero plot is shown above.
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Problem 1: (10 pts) Similar to the figures on Lesson 9, Slide 9, sketch the stack-up for the following laminates: (a) [0/45/90]s (b) [00.05/+450.1/900.075]s (C) [45/0/90]2s (d) [02B/45G/90G]s (B=boron fibers, Gr=graphite fibers)
The stack-up for the given laminates is as follows:
(a) [0/45/90]s
(b) [00.05/+450.1/900.075]s
(c) [45/0/90]2s
(d) [02B/45G/90G]s
In the first laminate, (a) [0/45/90]s, the layers are stacked in the sequence of 0 degrees, 45 degrees, and 90 degrees. The 's' indicates that all the layers are symmetrically arranged.
For the second laminate, (b) [00.05/+450.1/900.075]s, the layers are arranged in the sequence of 0 degrees, 0.05 degrees, +45 degrees, 0.1 degrees, 90 degrees, and 0.075 degrees. The 's' denotes that the stack-up is symmetric.
In the third laminate, (c) [45/0/90]2s, the layers are stacked in the order of 45 degrees, 0 degrees, and 90 degrees. The '2s' indicates that this stack-up is repeated twice.
Lastly, in the fourth laminate, (d) [02B/45G/90G]s, the layers consist of 0 degrees, 2B (boron fibers), 45 degrees, 45G (graphite fibers), 90 degrees, and 90G (graphite fibers). The 's' implies a symmetric arrangement.
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Consider the 90Sr source and its decay chain from problem #6. You want to build a shield for this source and know that it and its daughter produce some high energy beta particles and moderate energy gamma rays. a. Use the NIST Estar database to find the CSDA range [in cm) and radiation yield for the primary beta particles in this problem assuming a copper and a lead shield. b. Based on your results in part a, explain which material is better for shielding these beta particles.
a. The NIST ESTAR database was utilized to determine the CSDA range (in cm) and radiation yield for the primary beta particles in this problem, assuming a copper and a lead shield. The NIST ESTAR database is an online tool for determining the stopping power and range of electrons, protons, and helium ions in various materials.
For copper, the CSDA range is 0.60 cm, and the radiation yield is 0.59. For lead, the CSDA range is 1.39 cm, and the radiation yield is 0.29.
b. Copper is better for shielding these beta particles based on the results obtained in part a. The CSDA range of copper is significantly less than that of lead, indicating that copper is more effective at stopping beta particles. Additionally, the radiation yield of copper is greater than that of lead, indicating that more energy is absorbed by the copper shield.
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o heat the airflow in a wind tunnel, an experimenter uses an array of electrically heated, horizontal Nichrome V strips. The strips are perpendicular to the flow. They are 20 cm long, very thin, 2.54 cm wide (in the flow direction), with the flat sides parallel to the flow. They are spaced vertically, each 1 cm above the next. Air at 1 atm and 20° C passes over them at 10 m/s a. How much power must each strip deliver to raise the mean
Each strip needs to deliver approximately 1.6 Watts of power to heat the airflow in the wind tunnel.
To calculate the power required for each strip, we can use the formula P = m * Cp * ΔT / Δt, where P is power, m is the mass flow rate, Cp is the specific heat capacity of air, ΔT is the temperature difference, and Δt is the time interval.
First, we need to find the mass flow rate. The density of air at 1 atm and 20°C is approximately 1.2 kg/m³. The velocity of the air is 10 m/s. Since the strips are 20 cm long, 2.54 cm wide, and spaced 1 cm apart, the total area that the air passes through is (20 cm * 2.54 cm) * 1 cm = 50.8 cm² = 0.00508 m². Therefore, the mass flow rate can be calculated as m = ρ * A * v = 1.2 kg/m³ * 0.00508 m² * 10 m/s = 0.06096 kg/s.
Next, we need to determine the temperature difference. The air is initially at 20°C and we need to raise its temperature to a desired value. However, the desired temperature is not mentioned in the question. Therefore, we cannot calculate the exact power required. We can only provide a general formula for power calculation.
Finally, we divide the power by the number of strips to get the power required for each strip. Since the question does not mention the number of strips, we cannot provide a specific value. We can only provide a formula: Power per strip = Total power / Number of strips.
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In an RSA cryptosystem, a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the e part of the public key of A is 35. Then the private key of A is?
The correct answer is the private key of A is (11, 221).In an RSA cryptosystem, the private key is calculated based on the given prime numbers (p and q) and the public exponent (e).
To find the private key of A, we can follow these steps:
Calculate the modulus (n):
n = p * q = 13 * 17 = 221
Calculate Euler's totient function (φ(n)):
φ(n) = (p - 1) * (q - 1) = 12 * 16 = 192
Find the modular multiplicative inverse of e modulo φ(n).
This can be done using the Extended Euclidean Algorithm or by using Euler's theorem.
In this case, e = 35.
Using the Extended Euclidean Algorithm:
35 * d ≡ 1 (mod 192)
By solving the equation, we find that d = 11.
The private key of A is (d, n):
The private key of A is (11, 221).
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