For each question, choose the correct answer. 1 × 4 = 4 marks 1. The main difference between dynamic analysis and static analysis is that the former has a stream of solutions. True or false? 2. The difference equation defined by xt = 3 2 xt−1 + 5 7 xt−2 − 3 and x0 = 47, has a unique solution. True or false? 3. The sequence {xt}t defined by xt = 105 1+e t is bounded. True or false? 4. A divergent differential equation does not have a steady state solution. True or false?
For each question, choose the correct answer. 1 × 4 = 4 marks 1. The main...
I) For each question, choose the correct answer. 1x 4 = 4 marks 1. The main difference between dynamic analysis and static analysis is that the former has a stream of solutions. True or false? 2. The difference equation defined by 1: = -1 + 1-2-3 and zo = 47, has a unique solution. True or false? 3. The sequence {11}e defined by 21 = 100 is bounded. True or false? 4. A divergent differential equation does not have a...
1. The main difference between dynamic analysis and static analysis is that the former has a stream of solutions. True or false? 2. The difference equation defined by X+ = 347-1 + 27-2 – 3 and xo = 47, has a unique solution. True or false? 3. The sequence {xt}t defined by 2+ = is bounded. True or false? 4. A divergent differential equation does not have a steady state solution. True or false? 105 1+et
4) Answer with true or false 1) the force applied to the specimen in shear center was static( 2) the force applied to the specimen in buckling was dynamic ( ) 3) the force applied to the specimen in thin cylinder was static 4) the force applied to the specimen in deflection of beams was static)
4) Answer with true or false 1) the force applied to the specimen in shear center was static( 2) the force applied to the...
Answer all questions (especially part b if unable to do part
a)
QUESTION FOUR 25 MARKS] Consider the initial value problem d x()= A(0)x(t) +f(t), x(0) = xo where xo is some constant vector. A(T)dr A(t)= A(t)A()dr). Show that the matrix X (e) = ei A(0d (a) Assuming satisfies the matrix differential equation: Xt) = A(€)X(1) 10 Maris) (b) Obtain a solution to the initial value problem, given 0 A= f) x(0) -1 3 15 Marks
QUESTION FOUR 25 MARKS]...
Consider the differential equation
Use the drop-down menus to answer to determine whether the
following statements are TRUE or FALSE.
Question 2 7.5 / 10 pts Consider the differential equation y' + 3x~ y' + 6xy = 0. Use the drop-down menus to answer to determine whether the following statements are TRUE or FALSE. (1) y = -C3 = e is a solution of the differential equation for any constant c. False 3 (2) y = ce is a solution...
1 III) Consider the following differential equation: 5:(t)+32(t) - 4 = 0, 2(0) = 2. 1. Find the backward solution. 1,5 mark 2. Is this solution convergent or divergent? Justify your answer. mark 3. Determine the stationary solution and indicate whether it is stable or unstable. 1 mark 4. Sketch a phase diagram and a time-path diagram. 1,5 mark
(1) Answer True or False to the following questions: [ 4 points] a)1 pt Any solution method applicable to a single differential equation is also applicable T F to the solution of a set of differential equations. b)1 pt Analytical solutions can be found for most partial differential equations TF c) 1 pt The forward Euler's method (explicit) has a higher stability range than the T Backward Euler's method (implicit). e) 1 pt The shooting method requires an iterative procedure...
Solve the following questions and Choose the correct answer. 1) The General solution to y" + y = 0 sty -3&y(x) = -3 y = cos(3x) + sin(-31) , 3cos(x) – 3 sin(x) 3 ) 3 Answer 2) Suppose that y(t) and y(t) are two solutions of a certain second order linear differential equation, sin(t)y" + cos(t) y' - y = 0. 0<<< What is the general form of the Wronskian Wy ) (6) ? Without solving the equation. b)...
III) Consider the following differential equation: 5•(t) + 3x(t) - 4 = 0, x(0) = 2. 1. Find the backward solution. 2. Is this solution convergent or divergent? Justify your answer. 3. Determine the stationary solution and indicate whether it is stable or unstable. 4. Sketch a phase diagram and a time-path diagram.
Question 1 2 pts The Hermite Interpolation polynomial for 33 distinct nodes has Degree at most {Be Careful with the answer. Look at the Theorem and the Question Carefully; compare the given information} Question 2 2 pts If f € C4 [a, b] and p1, P2, P3, and p4 are Distinct Points in [a, b], Then 1. There are two 3rd divided differences 2. There is exactly one 3rd divided difference and it is equal to the value of f(iv)...