Final exam 2nd semetster 2019-2020 course Applied engineering maths (Quiz no 1) - ĐH Sư phạm Kỹ thuật

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Nội dung Text: Final exam 2nd semetster 2019-2020 course Applied engineering maths (Quiz no 1) - ĐH Sư phạm Kỹ thuật

HO CHI MINH CITY UNIVERSITY OFFINAL EXAM 2nd SEMESTER (2019 - 2020) TECHNOLOGY AND EDUCATION Course: APPLIED ENGINEERING MATIIS FACULTY OF MECHANICAL ENGINEERING Course code: AMME131529 Quiz No.: 01 No. of pages: 02 DEPARTMENT OF MECHATRONICS Duration: 90 minutes Open-book examination. Question 1: (4.0 points) A 1-lcg weight is attached to the lower end of a vertical spring-cylinder system, stretching it 1/3 inches. The weight is allowed to come to rest in the equilibrium position. At some later time, which we call time 0, the weight is struck a downward by an vertical force f(t) = H(t-l)x(2t+l). Given that the mathematical equation of the mechanical system as below: y” + 9y’ + 20y = f(t) Given that initial values of the system are y’(0) = 1; y(0) = 2. Use Laplace Transform method to determine the position variation of the weight y(t). Question 2: (3.0 points) To investigate the thermos-electric performance of a PV panel, an out-door experiment has been conducted. The PV panel is placed facing South and exposed to the Sun from 10:00am to 12:00am. The experimental data are given in the following Table 1. Table 1. Output power versus time of the tested PV panel t (minutes) 0 10 20 30 44 60 75 90 105 115 120 Output power (W) 1.1 1.5 3.5 2.8 4.0 1.7 3.7 5.1 5.0 4.7 4.1 a. Apply 3rd order Newton’s polynomial interpolation to find output power at 11:05am (which means t = 65). b. Employ Simpson 3/8, Simpson 1/3 and Trapezoidal integration models where most applicable to find the total output electricity energy amount produced by the PV panel within the 2 hours. Question 3: (3.0 points) Given the following equation system: 4-Xj_ x 4- 5 { + 2 * 2 + 2 6 * 4 = 2x t + x2 + 2 *3 + 5 *4 = 8 x \ + x 2 + 4*3 + *4 = 1 3x t + 2 *2 + 4* 3 + *4 = 6 a. Rewrite the system in matrix format A.X = B wherein X is the variable matrix, b. Find A '1. c. Make use of the results in b. to solve the equation system by Inverse matrix method. END. Note: Examiners are not allowed to explain quiz contents. Code No.: BM1/QT-PDBCL-RDTV Page: 1/2
Course Learning Outcomes Exant question [CLO 1.2]: Able to apply Laplace Transform method to solve differential Question 1 - integral equations. [CLO 1.3]: Able to apply mathematic methods to calculate, analyze and Question 1, 2, 3 investigate mechanical and mechatronic systems. [CLO 2.3]: Able to solve for polynomial interpolation methods when Question 2 testing mechanical systems. [CLO 4.1]: Able to calculate determinant, inverse matrix o f engineering Question 3 systems. Date: 07th July 2020 Code No.: BM1/QT-PDBCL-RDTV Page: 2/2