# ENT 300 exam III

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1. Does the variable (t) in the LT procedure have any physical significance?
yes, t is usually time
2. Can the TI-89 be used to determine the LT of all the common functions?
yes but it requires a manual step in the process
3. The range of (t) in the LT procedure is ___ to ____.
0, +infinity
4. The variable (t) in the LT procedure is a ______ variable.
real
5. The variable (s) in the LT procedure is a ______ variable.
complex
6. The inverse-Laplace transform process converts a _____ to a _______.
s-domain algebraic equation, time-domain algebraic equation
7. This LT procedure relies on
a LT table showing transform pairs of functions
8. The LT of y(t) is Y(s)
true
9. Is knowing the boundary condition necessary in the LT procedure of solving a DEQ?
yes
10. The fourth step of the Laplace transform procedure is:
time-domain solution of the DEQ
11. The third step of the Laplace transform procedure is:
s-domain solution of the DEQ
12. The second step of the Laplace transform procedure is:
s-domain version of the time-domain DEQ
13. The first step of the Laplace transform procedure is:
Time-domain DEQ
14. How many steps are indicated by the three processes?
4
15. Finding the time-domain solution of the original DEQ from the s-domain solution (i.e. taking the inverse Laplace transform) is the ____ process.
third
16. Solving the s-domain version of the DEQ for the s-domain solution is the ____ process.
second
17. Finding the s-domain version of the original DEQ (i.e. Laplace transform of the DEQ) is the ____ process.
first
18. How many processes are indicated by the arrows in the Laplace transform (LT) procedure for finding the solution of a DEQ?
3
19. Laplace transform of a time-domain function is _______-domain function.
an s
20. Integration in the time domain is quivalent to multiplication by _______ in the s domain.
1/s
21. Derivative in the time domain is quivalent to multiplication by _______ in the s domain
s
22. L{f''(t)} =
s^2 * L{f(t)} - s*f(0) - f(0)
23. L{f'(t)} =
s* L{f(t)} - f(0)
24. . L{a*f(t) + b*g(t)} = a*L{f(t)} + b*L{g(t)} due to the ______ of the Laplace Transform.
linearity
25. L{a*f(t)} = a*L{f(t)}
true
26. f(t)=t^n. L{f(t)}=
n!/s^(n+1)
27. f(t)=t. L{f(t)}=
1/s^2
28. f(t)=cos(a*t). L{f(t)}=
s/(s^2+a^2)
29. f(t)=sin(a*t). L{f(t)}=
a/(s^2+a^2)
30. f(t)=exp(a*t). For a less than s, L{f(t)}=
1/(s-a)
31. (t)=exp(-s*t). For s greater than zero, f(infinity)=
0
32. f(t)=exp(-s*t). f(0)=
1
33. f(t)=1. L{f(t)} =
1/s
34. L{f(t)} is the Laplace Transform of a function f(t) and is defined as integral( _____ dt) evaluated from ______.
exp(-s*t) * f(t), zero to infinity
35. A transform relates one set of functions to another set of
functions
36. A function relates one set of numbers to another set of
numbers
37. L{f(t)} is the Laplace Transform of a function f(t) and can be used to solve DEQs.
true
38. L{f(t)} is the Laplace Transform of a function f(t) and is very useful, especially in engineeing
true
39. The type of nonlinearity that has a one response when going up and a different response when going down is called
hysteresis
40. The type of nonlinearity that has zero output signal when the input signal is near zero is called
41. The type of nonlinearity that limits the output signal when the input signal becomes too large or too small is called
saturation
42. Numerical integration is required when non-linearities are inserted into the linear mass-spring-damper problem.
true
43. Numerical integration is required in the linear mass-spring-damper problem.
false
44. The classic mass-spring-damper model is
linear and yields manual and TI-89 solutions
45. Linear models are used in engineering because they give
both of these solutions that are relatively easy to calculate. a reasonable understanding of real engineering systems.
46. Numerical integration is common in engineering, especially for
nonlinear models, which can accurately model real systems
47. The DEQ (y'=x-y^2) has no standard solution, but slope fields are easily computed, and slope fields permit visualization of all solutions.
true
48. The slope of a solution of the DEQ (y'=x-y^2) that passes through (2,1) is
1
49. The slope of a solution of the DEQ (y'=x-y^2) that passes through (1,2) is
-3
50. The slope of a solution of the 1st-order DEQ (y'=x-y^2) is x-y^2 where x and y defines any point within the field.
true
51. The solution of a DEQ depends on the starting point, which is also called
boundary conditions
52. The solution of a DEQ is a
function
53. One way of visualizing many solutions of a DEQ, all in one graph is called
slope field
54. How may different solutions exist for any DEQ?
infinite
55. All the DEQs in this course are also Ordinary Differential Equations (ODEs), and none are Partial Differential Equations (PDEs).
true
56. Octave, Simulink, spreadsheet, and TI-89 examples in the video show how to solve y'=x-y^2.
true
57. The Euler method is a ___-step method, because only ____ calculations are performed at each step.
2,2
58. The next value of y is calculated assuming ____slope from the present value of y.
linear
59. The slope of y(x) is calculated from the DEQ
at every step in the solution
60. The initial value of y is
the boundary condition and must be known.
61. The type of integrator discussed in the video is
Euler
62. The simulation step size is delta-__.
x
63. In the DEQ (y'=x-y^2), x can be replaced by t, which means that y' is
dy/dt
64. In the DEQ (y'=x-y^2), y' is
dy/dx
65. In the DEQ (y'=x-y^2), the independent variable is ___ and the dependent variable is ___.
x,y
66. Numerical solutions of DEQs _______ to form the solution.
are computer generated step by step
67. Since standard methods for solving y'=x-y^2 all fail, we conclude:
numerical-solution methods must be used
68. y'=x-y^2 can be solved by the TI-89 using the deSolve() function.
false
69. y'=x-y^2 is 2nd-order linear DEQ.
false
70. y'=x-y^2 is a homogeneous DEQ.
false
71. y'=x-y^2 is a 1st-order linear DEQ.
false
72. . y'=x-y^2 is a Bernouli DEQ.
false
73. y'=x-y^2 is an linear DEQ.
false
74. y'=x-y^2 is an exact DEQ.
false
75. y'=x-y^2 is a separable DEQ.
false
76. y'=x-y^2 is a special DEQ because ____ exist that describe the solution.
no combination of fundamental functions
77. The function y(x)=exp(m*x)*sin(w*x) (m<0, w>0, x>0) is known as
a damped sinusoid
78. For positive x and negative m, the function y(x)=exp(m*x) has an final value y(infinity)=
0
79. The common meaning of x in y(x)=exp(m*x) (m<0, x>0, in electrical circuits) is
time (seconds)
80. The common meaning of x in y(x)=exp(m*x) (m<0, x>0, in mechanical vibrations) is
position may be more common, but time is also possible
81. For positive x and negative m, the function y(x)=exp(m*x) has an initial value y(0)=
1
82. Characteristic equation real parts of roots for real systems are always
negative
83. If an equation that describes a real system (electrical or mechanical) becomes infinite, then
something has gone wrong.
84. The function y(x)=exp(m*x) will never become infinite for positive x if m is
negative
85. The function y(x)=exp(m*x) will become infinite for positive x if m is
positive
86. If the roots of the characteristic equation are D=m+i*w and D=m-i*w (complex conjugate pair), the solution of the 2nd order linear DEQ is
y=exp(m*x)*( C1*sin(w*x)+C2*cos(w*x) )
87. If the roots of the characteristic equation are D=k and D=k (same real number), the solution of the 2nd order linear DEQ is
y=C1*exp(k*x) + C2*x*exp(k*x)
88. If the roots of the characteristic equation are D=g and D=h (real numbers), the solution of the 2nd order linear DEQ is
y=C1*exp(g*x) + C2*exp(h*x)
89. The types of roots of the characteristic equation can be
non-repeated real, repeated real, and complex conjugate pair
90. ____ is the number of types of roots of the characteristic equation.
3
91. ____ is the number of roots of the characteristic equation.
2
characteristic equation
differential operator
94. a*y''+b*y'+c*y=0 is a special DEQ that can be written as (aD^2+bD+c)y=0 if D is defined as
d/dx
95. a*y''+b*y'+c*y=0 is a special DEQ of type ______, and all questions in this quiz are about this type of DEQ where a,b and c are constants.
2nd order linear with constant coefficients and the RHS is zero
96. Is y''=4/x separable, exact, 1st order linear, Bernouli DEQ?
yes, no, no, no
97. Is y'+y/x=-40x*y^2 separable, exact, 1st order linear, Bernouli DEQ?
no, no, no, yes
98. Is y'+x*y=83x separable, exact, 1st order linear, Bernouli DEQ?
yes, no, yes, no
99. Is y'+y/x=83x separable, exact, 1st order linear, Bernouli DEQ?
no, yes, yes, no
100. Almost all the manual work in finding DEQ solutions is in
the algebra
101. The type of DEQ that permits the easiest manual solution
variables can be separated
102. y*dx+x*dy is equivalent to ____ and may yield an exact DEQ.
d(x*y)
103. (y*dx-x*dy)/y^2 is equivalent to ____ and may yield an exact DEQ.
d(x/y)
104. (x*dy-y*dx)/x^2 is equivalent to ____ and may yield an exact DEQ.
d(y/x)
105. Constants of integration can be determined if ______ are known.
boundary conditions
106. The DEQ 5x+y-yy'=0 will have _____ constants of integration.
1
107. ln(A) + ln(B) =
ln(A*B)
108. C is the constant of integration. Replacing 9C with C is ok because C is
an unknown constant
109. The homogeneous DEQ (5x+y)dx + (-y)dy = 0 can be manually solved if the substitution is introduced
y=v*x
110. If y=v*x, then dy=
v*dx+x*dv
111. Is xy homogeneous? Is x*y^2 homogeneous?
yes, no
112. If the DEQ M dx + N dy =0 where M & N are functions of x & y and M & N are homogeneous of the same degree, then the DEQ is
homogeneous
113. The DEQ (5x+y)dx + (-y)dy = 0 is in the form
M dx + N dy =0
114. Is the DEQ 5x+y-yy'=0 equivalent to: (5x+y)dx + (-y)dy = 0?
yes
115. The following homogeneous DEQ can be recognized if put into this form
(5x+y)dx + (-y)dy = 0
116. The MKS units of voltage is
Volt
117. The MKS units of electrical current is
Ampere
118. The MKS units of resistance is
Ohm
119. The MKS units of inductance is
Henry
120. The MKS units of capacitance is
121. The DEQ for the electrical circuit has the dependent variable _____ and indepenent variable _____.
capacitor voltage, time
122. The DEQ for the electrical circuit is based on
Kirchhoff's voltage law
123. i(t)=C*V(t)' is the current-voltage relationship for a(an)
capacitor
124. i(t)=v(t)/R is the current-voltage relationship for a(an)
resisitor
125. V(t)=L*i(t)' is the current-voltage relationship for a(an)
inductor
126. The position of the sliding mass is derived from
a differential equation based on Newton's second law
127. Position is the integral of _____, assuming the appropriate constant of integration.
velocity
128. Velocity is the rate of change of
position
129. The mks unit of mass is ____ and acceleration is _____ in F=m*a is
kilograms, meters/second^2
130. The basic equation that describes the sliding mass is Newton's
2nd law: F=m*a
131. The damper force on the sliding mass is F =
b * y' where b is the damper constant and y' is the speed
132. The spring force on the sliding mass is F =
k * y where y is the horizontal position and k is the spring constant

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 Author: lacythecoolest ID: 312255 Filename: ENT 300 exam III Updated: 2015-11-30 17:34:33 Tags: engineering Folders: Description: 3rd exam, stopped at 9067 Show Answers:

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