Section 1: Problem Definition One-Dimensional Unconstrained Optimization / Newton's Method Refer to the textbook or other references specified in the course syllabus, read about Newton's method for One-Dimensional Unconstrained Optimization and solve the following problem: The torque transmitted to an induction motor is a function of the slip between the rotation of the stator field and the rotor speed s where slip is defined as: 11 where n = revolutions per second of rotating stator speed and ne = rotor speed. Kirchhoff's laws can be used to show that the torque (expressed in dimensionless forn) and slip are related by: 1503-3) T = (1 - 3)(432 - 3x + 4) Use Newton's method to determine the slip at which the maximum torque occurs. Start with an initial value of 0.1 and 8 = 0.001%

Using the moment distribution method to solve the beam shown below. Take w = 24 kN/m and q = 9 kN/m. q A 2E1 B EI с EI D 4 m 4 m 3 m = Part 1 Calculate the fixed end moments at points B and C: a) FEM kN m b) FEM kNm c) FEM kN m d) FEM kNm = = Part 2 Calculate the distribution factors: a) DFBA = b) DFBC c) DFCB d) DFCD = Part 3 What is the moment that is carried over from B to C at the first iteration of the solution (start the iteration from point B)? M= kN m

Part 4 Calculate the moment at B and indicate which face of the beam is under tension at that point: a) MB kN m =

Question 4 (Total Weight 25%) Consider the rod of Fig. 24. The length of the rod is 1.2-m and its mass is 25 kg. The ends A and B of the rod can move freely and with no friction along two straight tracks. The rod is released with no velocity from the position shown. It is required to: (i). Determine the acceleration of points A and B graphically assuming that the angular acceleration of the rod is 2.33 rad/s2. (Weight 10%) Determine the acceleration of point G. (Weight 10%) Determine the reactions at points A and B. (Weight 5%) (ii). (iii). В. 1.2 m G B = 45° 30°f| А D Fig. 24

3) Draw the chair conformations of the following compound? CHE H

Question: Design a digital FIR lowpass filter (with the following specifications): wo = 0.21, R, = 0.25 dB, w, = 0.31, A, - 50 dB Choose an appropriate window function from Table 7.1 of book "Digital signal processing using MATLAB" 3rd edition by Vinay K. Ingle and John G. Proakis. (0) Plot the impulse response and provide a plot of the frequency response of the designed filter (ii) Chose an input signal of your choice (plot it as well) and show filtered signal. Do this for both: first by adjusting frequency of input signal within pass band and then adjusting it into stop band (iii) show all the steps "how to perform part (ii)" using code composer studio

Simplify the query given bellow SELECT Name FROM Faculty WHERE POSITION = "DD" AND STAFFNO="F1021" AND SALARY=70000 AND STAFFNO="F1021" OR SALARY! = 70000 (! = indicate not equal)?

Q#2: a- What tests would you specify to ensure if the cement supplied at the site is of good quality? Write the importance of each test in 1 or 2 lines. b- State the conditions under which you will recommend the following cements. Give also the reasons. (i) Low heat Portland cement (i) Rapid hardening cement (iii) Air entraining cement

1. a) 0.5 kg of ice at 0'C is dropped into 2 kg of water at 50 °C. Find final temperature of system(2p)(Cwater =4186J/kg ⓇC Cic=2093J/kg °C, LF 3.33 x 10ʻJ/ kg, Lx=2260 J/kg) b) How much heat is required to increase temperature of 1 kg ice at -20°C to 120 °C?(2p)