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Trang 1HO CHI MINH CITY UNIVERSITY OF
TECHNOLOGY AND EDUCATION
FACULTY OF MECHANICAL ENGINEERING
DEPARTMENT OF MECHATRONICS
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 o f the mechanical system as below:
y” + 9y’ + 20y = f(t) Given that initial values o f 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 o f the tested PV panel
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_ + 2 * 2 + x 2 4- 6 * 4 = 5
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.
FINAL EXAM 2nd SEMESTER (2019 - 2020) Course: APPLIED ENGINEERING MATIIS
Course code: AMME131529
Duration: 90 minutes Open-book examination
Trang 2Course Learning Outcomes Exant question [CLO 1.2]: Able to apply Laplace Transform method to solve differential
- integral equations
Question 1 [CLO 1.3]: Able to apply mathematic methods to calculate, analyze and
investigate mechanical and mechatronic systems
Question 1, 2, 3 [CLO 2.3]: Able to solve for polynomial interpolation methods when
testing mechanical systems
Question 2
[CLO 4.1]: A ble to calculate determinant, inverse matrix o f engineering
system s.
Question 3
Date: 07th July 2020