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Does the variable (t) in the LT procedure have any physical significance?
yes, t is usually time

Can the TI89 be used to determine the LT of all the common functions?
yes but it requires a manual step in the process

The range of (t) in the LT procedure is ___ to ____.
0, +infinity

The variable (t) in the LT procedure is a ______ variable.
real

The variable (s) in the LT procedure is a ______ variable.
complex

The inverseLaplace transform process converts a _____ to a _______.
sdomain algebraic equation, timedomain algebraic equation

This LT procedure relies on
a LT table showing transform pairs of functions

The LT of y(t) is Y(s)
true

Is knowing the boundary condition necessary in the LT procedure of solving a DEQ?
yes

The fourth step of the Laplace transform procedure is:
timedomain solution of the DEQ

The third step of the Laplace transform procedure is:
sdomain solution of the DEQ

The second step of the Laplace transform procedure is:
sdomain version of the timedomain DEQ

The first step of the Laplace transform procedure is:
Timedomain DEQ

How many steps are indicated by the three processes?
4

Finding the timedomain solution of the original DEQ from the sdomain solution (i.e. taking the inverse Laplace transform) is the ____ process.
third

Solving the sdomain version of the DEQ for the sdomain solution is the ____ process.
second

Finding the sdomain version of the original DEQ (i.e. Laplace transform of the DEQ) is the ____ process.
first

How many processes are indicated by the arrows in the Laplace transform (LT) procedure for finding the solution of a DEQ?
3

Laplace transform of a timedomain function is _______domain function.
an s

Integration in the time domain is quivalent to multiplication by _______ in the s domain.
1/s

Derivative in the time domain is quivalent to multiplication by _______ in the s domain
s

L{f''(t)} =
s^2 * L{f(t)}  s*f(0)  f(0)

L{f'(t)} =
s* L{f(t)}  f(0)

. L{a*f(t) + b*g(t)} = a*L{f(t)} + b*L{g(t)} due to the ______ of the Laplace Transform.
linearity

L{a*f(t)} = a*L{f(t)}
true

f(t)=t^n. L{f(t)}=
n!/s^(n+1)


f(t)=cos(a*t). L{f(t)}=
s/(s^2+a^2)

f(t)=sin(a*t). L{f(t)}=
a/(s^2+a^2)

f(t)=exp(a*t). For a less than s, L{f(t)}=
1/(sa)

(t)=exp(s*t). For s greater than zero, f(infinity)=
0



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

A transform relates one set of functions to another set of
functions

A function relates one set of numbers to another set of
numbers

L{f(t)} is the Laplace Transform of a function f(t) and can be used to solve DEQs.
true

L{f(t)} is the Laplace Transform of a function f(t) and is very useful, especially in engineeing
true

The type of nonlinearity that has a one response when going up and a different response when going down is called
hysteresis

The type of nonlinearity that has zero output signal when the input signal is near zero is called
dead zone

The type of nonlinearity that limits the output signal when the input signal becomes too large or too small is called
saturation

Numerical integration is required when nonlinearities are inserted into the linear massspringdamper problem.
true

Numerical integration is required in the linear massspringdamper problem.
false

The classic massspringdamper model is
linear and yields manual and TI89 solutions

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.

Numerical integration is common in engineering, especially for
nonlinear models, which can accurately model real systems

The DEQ (y'=xy^2) has no standard solution, but slope fields are easily computed, and slope fields permit visualization of all solutions.
true

The slope of a solution of the DEQ (y'=xy^2) that passes through (2,1) is
1

The slope of a solution of the DEQ (y'=xy^2) that passes through (1,2) is
3

The slope of a solution of the 1storder DEQ (y'=xy^2) is xy^2 where x and y defines any point within the field.
true

The solution of a DEQ depends on the starting point, which is also called
boundary conditions

The solution of a DEQ is a
function

One way of visualizing many solutions of a DEQ, all in one graph is called
slope field

How may different solutions exist for any DEQ?
infinite

All the DEQs in this course are also Ordinary Differential Equations (ODEs), and none are Partial Differential Equations (PDEs).
true

Octave, Simulink, spreadsheet, and TI89 examples in the video show how to solve y'=xy^2.
true

The Euler method is a ___step method, because only ____ calculations are performed at each step.
2,2

The next value of y is calculated assuming ____slope from the present value of y.
linear

The slope of y(x) is calculated from the DEQ
at every step in the solution

The initial value of y is
the boundary condition and must be known.

The type of integrator discussed in the video is
Euler

The simulation step size is delta__.
x

In the DEQ (y'=xy^2), x can be replaced by t, which means that y' is
dy/dt

In the DEQ (y'=xy^2), y' is
dy/dx

In the DEQ (y'=xy^2), the independent variable is ___ and the dependent variable is ___.
x,y

Numerical solutions of DEQs _______ to form the solution.
are computer generated step by step

Since standard methods for solving y'=xy^2 all fail, we conclude:
numericalsolution methods must be used

y'=xy^2 can be solved by the TI89 using the deSolve() function.
false

y'=xy^2 is 2ndorder linear DEQ.
false

y'=xy^2 is a homogeneous DEQ.
false

y'=xy^2 is a 1storder linear DEQ.
false

. y'=xy^2 is a Bernouli DEQ.
false

y'=xy^2 is an linear DEQ.
false

y'=xy^2 is an exact DEQ.
false

y'=xy^2 is a separable DEQ.
false

y'=xy^2 is a special DEQ because ____ exist that describe the solution.
no combination of fundamental functions

The function y(x)=exp(m*x)*sin(w*x) (m<0, w>0, x>0) is known as
a damped sinusoid

For positive x and negative m, the function y(x)=exp(m*x) has an final value y(infinity)=
0

The common meaning of x in y(x)=exp(m*x) (m<0, x>0, in electrical circuits) is
time (seconds)

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

For positive x and negative m, the function y(x)=exp(m*x) has an initial value y(0)=
1

Characteristic equation real parts of roots for real systems are always
negative

If an equation that describes a real system (electrical or mechanical) becomes infinite, then
something has gone wrong.

The function y(x)=exp(m*x) will never become infinite for positive x if m is
negative

The function y(x)=exp(m*x) will become infinite for positive x if m is
positive

If the roots of the characteristic equation are D=m+i*w and D=mi*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) )

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)

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)

The types of roots of the characteristic equation can be
nonrepeated real, repeated real, and complex conjugate pair

____ is the number of types of roots of the characteristic equation.
3

____ is the number of roots of the characteristic equation.
2

(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

(aD^2+bD+c)y=0 is a DEQ. (aD^2+bD+c) is called a/an
differential operator

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

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

Is y''=4/x separable, exact, 1st order linear, Bernouli DEQ?
yes, no, no, no

Is y'+y/x=40x*y^2 separable, exact, 1st order linear, Bernouli DEQ?
no, no, no, yes

Is y'+x*y=83x separable, exact, 1st order linear, Bernouli DEQ?
yes, no, yes, no

Is y'+y/x=83x separable, exact, 1st order linear, Bernouli DEQ?
no, yes, yes, no

Almost all the manual work in finding DEQ solutions is in
the algebra

The type of DEQ that permits the easiest manual solution
variables can be separated

y*dx+x*dy is equivalent to ____ and may yield an exact DEQ.
d(x*y)

(y*dxx*dy)/y^2 is equivalent to ____ and may yield an exact DEQ.
d(x/y)

(x*dyy*dx)/x^2 is equivalent to ____ and may yield an exact DEQ.
d(y/x)

Constants of integration can be determined if ______ are known.
boundary conditions

The DEQ 5x+yyy'=0 will have _____ constants of integration.
1


C is the constant of integration. Replacing 9C with C is ok because C is
an unknown constant

The homogeneous DEQ (5x+y)dx + (y)dy = 0 can be manually solved if the substitution is introduced
y=v*x

If y=v*x, then dy=
v*dx+x*dv

Is xy homogeneous? Is x*y^2 homogeneous?
yes, no

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

The DEQ (5x+y)dx + (y)dy = 0 is in the form
M dx + N dy =0

Is the DEQ 5x+yyy'=0 equivalent to: (5x+y)dx + (y)dy = 0?
yes

The following homogeneous DEQ can be recognized if put into this form
(5x+y)dx + (y)dy = 0

The MKS units of voltage is
Volt

The MKS units of electrical current is
Ampere

The MKS units of resistance is
Ohm

The MKS units of inductance is
Henry

The MKS units of capacitance is
Farad

The DEQ for the electrical circuit has the dependent variable _____ and indepenent variable _____.
capacitor voltage, time

The DEQ for the electrical circuit is based on
Kirchhoff's voltage law

i(t)=C*V(t)' is the currentvoltage relationship for a(an)
capacitor

i(t)=v(t)/R is the currentvoltage relationship for a(an)
resisitor

V(t)=L*i(t)' is the currentvoltage relationship for a(an)
inductor

The position of the sliding mass is derived from
a differential equation based on Newton's second law

Position is the integral of _____, assuming the appropriate constant of integration.
velocity

Velocity is the rate of change of
position

The mks unit of mass is ____ and acceleration is _____ in F=m*a is
kilograms, meters/second^2

The basic equation that describes the sliding mass is Newton's
2nd law: F=m*a

The damper force on the sliding mass is F =
b * y' where b is the damper constant and y' is the speed

The spring force on the sliding mass is F =
k * y where y is the horizontal position and k is the spring constant

