Assignment 12 Solutions: These book solutions complex form follow the standard format. If you follow
our notes then replace i with -i and things will match up for you.
12.3 #19.
12.3 #21.
12.4 #4.
ENGM2022: Assignment 12: Winter Term 2017
1. Chapter 12.3, #19.
2. Chapter 12.3, #21.
3. Chapter 12.4 #4.
4. Use the fourier series from problem #1 as the periodic external forcing f (t) of a criticallydamped spring mass system d2 y/dt2 + 2dy/dt + y = f (
ENGM2022: Assignment 11: Winter Term 2017
1. Use Laplace Transforms to solve d2 y/dt2 + 2dy/dt + y = f (t), where at t = 0, y = y0 and
at t = 0, dy/dt = v0 . Write the inverse of the portion involving the Laplace Transform as a
convolution. Write out your
ENGM2022: Assignment 7 Solutions: Winter Term 2017
1. In the following problems find the transform Lcfw_f (t):
a) L cfw_t(sin t) =
(s2
b) L cfw_sinh kt =
s2
2s
+ 1)2
k
k2
n
o
3!
2
3
1
+
3
+
+
s4
s3 s2 s
c) L t3 + 3t2 + 3t + 1 =
d) L cfw_sin 2t cos 2t = L
ENGM 2022
Assignment 8 Part 2
2017
Problem 4. Consider the piecewise function f (t) = t2 , 0 t a, f (t) = t, a t b, and
f (t) = 0, t b. Assume that a < b.
Find the heaviside function format for f (t).
Find the Laplace transform of f (t) using R54 in the
ENGM2032, Applied Probability and Statistics
Fall 2016
Assignment #9: Solutions
1) a) In order to conclude (i.e., prove) that the mean contaminant level, c , is in excess of the
maximum allowable, what the agency wants to conclude must be put into the alt
ENGM2032, Applied Probability and Statistics
Fall 2016
Assignment #6: Solutions
1) We will assume that stocks perform independently, and that they have a constant probability
that their first year returns exceed expectation. Then the number of stocks havi
ENGM2032, Applied Probability and Statistics
Fall 2016
Assignment #5: Solutions
1) Let Nn be the number of defective rods in a lot of n. Assuming that the rods are independent
with a constant probability of being substandard, Bernoulli trials can be used,
ENGM2032, Applied Probability and Statistics
Fall 2016
Assignment #7: Solutions
1) Reading from table A.2 for = 9 we get,
a) P T < 3.250 = 1
P T > 3.250 = 1
b) P 1.833 < T < 3.690 = 0.05
c) P T <
d) P
0.005 = 0.995
0.0025 = 0.0475
1.383 = P T > 1.383 = 0.
ENGM2032, Applied Probability and Statistics
Fall 2016
Assignment #9
Due: Tue Dec 6, 2016
1) A government agency wants to determine whether the mean radium-226 concentration in the
coolant discharge from a nuclear reactor is greater than the maximum allow
ENGM2032, Applied Probability and Statistics
Fall 2016
Assignment #7
Due: Thu Nov 17, 2016
1) This question exercises the use of the t and 2 distribution tables. Suppose that T has a
t-distribution with 9 degrees of freedom. Then what is
a) P T < 3.250 ?
ENGM2032, Applied Probability and Statistics
Fall 2016
Assignment #8
Due: Thu Nov 24, 2016
1) A machine is punching holes in plastic parts coming along an assembly line. A sample of the
plastic parts is taken and the hole diameters are 1.01, 0.97, 1.03, 1
ENGM2032, Applied Probability and Statistics
Fall 2016
Assignment #8: Solutions
1) We have n = 9 diameter observations, from which we can compute
1X
xi
x=
n
n
i=1
= (1.01 + 0.97 + 1.03 + 1.04 + 0.99 + 0.98 + 0.99 + 1.01 + 1.03)/9 = 1.00556
s2 =
"
n
1
h
#
1
Assignment 4
Department of Engineering Mathematics and Internetworking
COMPUTER PROGRAMMING
ENGM 1081
ASSIGNMENT 4
Due Date: Tuesday, October 10, 2017, 10:00 am
1. Write a program, derivative.c, to approximate the derivatives of ex , cos(x) and sin(x) a
ENGM2032, Applied Probability and Statistics
Fall 2014
Assignment #9
Due: Tuesday, Dec 2, 2014
1) The manufacturer of a certain chemical claims that the amount of the impurities in the chemical
does not exceed 4%. You, however, are suspicious about this c
ENGM2032, Applied Probability and Statistics
Fall 2014
Assignment #3
Due: Thursday, Oct 2, 2014
1) At a particular intersection, the probability that the traffic lights are functioning properly is 0.95. If
the traffic lights are functioning properly, the
ENGM2032, Applied Probability and Statistics
Fall 2014
Assignment #8
Due: Thursday, Nov 20, 2014
1) The performance of a yogurt dispenser is investigated. The target amount for which the
dispenser is calibrated is 50 ml. However, 25 measurements of the ac
ENGM2032, Applied Probability and Statistics
Fall 2014
Assignment #1
Due: Thursday, Sep 18, 2014
1) The fuel economy of two small cars is being studied by driving 15 of each in different conditions
and recording the fuel consumed. The resulting fuel econo