MATERIALS SCIENCE & ENGINEERING:AN INTRO
10th Edition
ISBN: 9798203933584
Author: Callister
Publisher: ZYBOOKS
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H.W:
1. Find the center of mass and the moment of inertia and radius of
gyration about the y-axis of thin rectangular plate cut from the first
quadrant by the lines x = 6 and y = 1 if (x, y) = x+y+1
2. Find the moment of inertia and radius of gyration about
the coordinate axes of a thin rectangular plate of constant density &
bounded by the lines x = 3 and y = 3 in the first quadrant.
Example find f(t)?
-4s
F(s)=
(s² + 4)²
The first photo is question 1
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- a) Write down the order of the transfer function in each of the following cases. Assume that there are no terms in the numerator that will cancel terms in the denominator. 10 H(s) H(s) = s+1 5 (s+3)(s—. 4) 4s1 5 H(s) = H(s) - 83 +1 s27s 6 H(s) H(s) = s(s²+4s) 2s27s+1 84583882 +3s+2 H(s) 83 +8 s+1 = H(s) s34s26s+5 s52s4383 + 4s2 +5s +6arrow_forwardQuestion 5 ( A system is found to have zeros of -3 and poles of 4, and -2. The system also has a gain of 4. Write out the corresponding transfer function. Question 6. A system has a transfer function of What is the gain, K, of the system? Question 7 ( A system has a transfer function of H(s) - 4 8+5 H(s): = 4 8 +5 A step input of size 3 is applied to the system at time zero (Since we're dealing with transfer functions, x(0) is also zero at time zero). a) [10] What is the response ✗(s) of the system? b) [10] Derive the time dependent solution, x(t), of this responsearrow_forwardNote: You might want to do the last question first because the last question asks you to write some python code to calculate the zeros and poles. You could use that code here to help you (except the first problem which you should be able to do by inspection alone) Find the poles and zeros for each of the following transfer functions 1. S+3 H(s) = 8 5 2. H(s): = s238 +1 s2 +48 +3 3. s(s+4) H(s) s3+2s23s 4. 82-586 H(s) = - 8382-68 5. H(s): = s2 +48 +3 s45836s2 - 6arrow_forward
- Write python program to plot the zeros and poles if a user provides the coefficients for the numerator and denominator of the transfer function. Since the zeros and poles can be complex, this plot is essentially and argand diagram, where the x axis is the real component and the y axis the imaginary component of a given zero or pole. Create a method called plot-poles zeros(num, den) which takes two lists containing the coefficients. Here is an example and the resulting plot. num [1, 3, 7] # yields zeros at -1.5 +/- 2.17945j den = [1, 4, 5, 3] # yields poles at -2.46557, -0.7672143 +/- 0.7925519j plot_poles_zeros(num, den) Imaginary Page 2 Pole-Zero Plot 3 Zeros × Poles 2 1 -2 1 * Real When you write your code you are only allowed to use the packages numpy and matplotlib. Make sure you label the axes, provide a legend and give a title to your plot (See the example plot). Hint: numpy has a method called roots. When given a list of numbers corresponding to the coefficients of a polynomial,…arrow_forwarda) [10] Compute the zeros and poles for the following transfer function: $2 +5s+6 H(s): s2 +3s+2 b) [10] Factor both polynomials in the numerator and denominator. What does this tell you about one of the poles and zeros you found in a)?arrow_forwardWhat kind of boundary must a system have to undergo the stated Interaction with its surroundings if possible ( mention the 3 qualities of the boundary in each case A. WORK INTERACTIONS ONLY B. MASS AND HEAT INTERACTIONS ONLY C. HEAT INTERACTIONS ONLY IS THIS POSSIBLE, EXPLAIN. D. WORK AND MASS INTERACTIONS ONLY. E. WORK AND HEAT INTERACTIONS ONLY F. MASS INTERACTIONS ONLY. IS THIS POSSIBLE OR NOT. EXPLAINarrow_forward
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