ENT 300 exam III

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lacythecoolest
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312255
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ENT 300 exam III
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2015-11-30 12:34:33
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engineering
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3rd exam, stopped at 9067
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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
    dead zone
  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
  92. (aD^2+bD+c) in the DEQ (aD^2+bD+c)y=0 can form the equation (aD^2+bD+c)=0, which is called
    characteristic equation
  93. (aD^2+bD+c)y=0 is a DEQ. (aD^2+bD+c) is called a/an
    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
    Farad
  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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