Assignment 3 1. In a combustor, butane (C4H10) is used as the fuel with an air fuel ratio of 22, by mass. Calculate the fuel utilization efficiency of this process if the exhaust gas has a temperature
The Hong Kong Polytechnic University
Department of Mechanical Engineering
2008/09 Semester 1 ME4204 Mechatronic Systems
Quiz 1 Student Name: Programme Code: Student ID: Date:
Please answer ALL the que
ME4204 08/09 Semester 1
The Hong Kong Polytechnic University
Department of Mechanical Engineering
2008/09 Semester 1
ME4204 Mechatronics Systems Mini-Project Objective To enhance students understandin
ma2176 a4 Brief Sol Integration and its Applications 1.
x 3 x if 0 x < 1 . Find F ( x) = f (t )dt , 0 x 2 . Let f ( x) = 2 + x if 1 x 2 0
Solution: For 0 x < 1 , F ( x) = f ( t ) dt = ( 3 t ) dt = 3 x
ma2176 a4 Integration and its Applications
x 3 x if 0 x < 1 . Find F ( x) = f (t )dt , 0 x 2 . 1. Let f ( x) = 2 + x if 1 x 2 0
2. Evaluate the following integrals: x +1 (a) dx x 3. Evaluate the follo
ma2176 a3 sol Applications of Derivatives 1. An airplane, flying horizontally at an altitude of 1 km, passes directly over an observer. If the constant speed of the plane is 240 km per hour, how fast
ma2176 a3 1.
Applications of Derivatives
An airplane, flying horizontally at an altitude of 1 km, passes directly over an observer. If the constant speed of the plane is 240 km per hour, how fast is i
ma2176 a2 sol Derivatives 1. If y = x sin x , prove that x 2 y ' 2 xy '+ 2 + x 2 y = 0 .
(
)
Proof: y = x sin x y ' = sin x + x cos x y " = cos x + cos x x sin x = 2 cos x x sin x . So x 2 y ' 2 xy '+
ma2176 a2 1.
Derivatives
If y = x sin x , prove that x 2 y ' 2 xy '+ 2 + x 2 y = 0 .
(
)
2. 3.
If u = ax 2 + 2bx + c , prove that
d 2ax 2 + 3bx + c ( xu ) = . dx u
Differentiate the following function
ma2176 a1 sol Functions, Limits and Continuity 1. Find the largest possible domain of each of the following functions: 2x , (b) y = f ( x) = 25 x 2 , (c) (a) y = f ( x) = 2 x 4x 5
( x) =
x2 1 x 1
Sol
ma2176 a1 1.
Functions, Limits and Continuity
Find the largest possible domain of each of the following functions: x2 1 2x , (b) y = f ( x) = 25 x 2 , (c) ( x) = (a) y = f ( x) = 2 x 1 x 4x 5
2.
Let f
Design and Manufacturing I (ME3204)
Test Name: ID: Question (a) Complete the profit model for a consumer product as shown in the following table. (8 marks)
Year Sales Price Number of units sold Net Sa
ma2176 a5 Brief Sol Complex Numbers 1. Find the square roots of 5 12i .
Solution: 2 If 5 12i = a + bi , then 5 12i = ( a + bi ) = a 2 b2 + 2abi .
a 2 b 2 = 5 . Thus, the solutions to Equating the real
ME 4905 2008 Advanced Numerical Methods for Engineers Homework 1 (Due date: 16 Sept in the class) 1. If the determinant of the coefficient matrix A is zero, what can you say about the system? 2. Consi
Supplement: Finite Difference
1. Finite difference method
The complete governing equations in boundary layer:
u v + =0 x y
(1)
u
u u 2u +v = g(T - T) + x y y 2
(2)
u
2T T T +v = y x y 2
(3)
For an an
ME 4905 Advanced Numerical Methods
Fourier Approximation
Lecturer: T.Y. Ng (PhD) Email: [email protected]
Introduction
Engineers often deal with systems that oscillate or vibrate. Therefore trigonome
ME 4905 Advanced Numerical Methods
Least-Squares Regression
Lecturer: T.Y. Ng (PhD) Email: [email protected]
Curve Fitting
Describes techniques to fit curves (curve fitting) to discrete data to obtai
The Hong Kong Polytechnic University
Department of Mechanical Engineering
2008/09 Semester 1 ME4204 Mechatronics Systems
Assignment 2 Name: Student ID:
Notes: 1. Please answer all the following questi
The Hong Kong Polytechnic University
Department of Mechanical Engineering
2008/09 Semester 1 ME4204 Mechatronic Systems
Quiz 2 Student Name: Programme Code: Student ID: Date:
Notes: Please answer ALL
The Hong Kong Polytechnic University
Department of Mechanical Engineering
2008/09 Semester 1 ME4204 Mechatronics Systems
Assignment 1 Name: Student ID:
1. Find out the currents through R1 and R3 in th
The Hong Kong Polytechnic University
Department of Mechanical Engineering
2008/09 Semester 1 ME4204 Mechatronics Systems
Assignment 2 Name: Student ID:
Notes: 1. Please answer all the following questi
The Hong Kong Polytechnic University
Department of Mechanical Engineering
2008/09 Semester 1 ME4204 Mechatronics Systems
Assignment 1 Name: Student ID:
1. Find out the currents through R1 and R3 in th
ME4204 Mechatronic Systems
2008/09 Semester 1 Review
Topics
1. 2. 3. 4. 5. 6. 7. 8. 9. Introduction of Mechatronic Systems Electrical Components of Mechatronic Systems Sensors and Transducers Part 1 S