30 Questions
Which step in the analysis and design sequence involves obtaining the system's schematic?
Developing mathematical models from schematics
What are the two methods discussed for developing mathematical models from schematics?
Transfer functions and state equations
Which fundamental physical laws are applied when modeling electrical networks?
Ohm's law and Kirchhoff's laws
What type of equation can describe the relationship between the input and output of a system?
Differential equation
What is the purpose of the coefficients in a differential equation?
Formulation or description of the system
Which of the following is a characteristic of an operational amplifier?
Differential output
What are the three passive linear components in electric circuits?
Resistors, capacitors, and inductors
What is the transfer function for an electrical component that represents an equivalent differential equation?
Impedance
Which method involves summing voltages around loops or meshes to obtain transfer functions?
Loop or mesh analysis
What can be used to implement transfer functions in electrical circuits?
Operational amplifiers
Which of the following is a passive, linear component in mechanical systems?
Spring
What is the analogy between the spring and the capacitor?
Both store energy
What is the analogy between mechanical force and electrical voltage?
Mechanical force is analogous to electrical voltage
How many differential equations are required to describe a mechanical system with multiple linearly independent motions?
Two
What is the number of linearly independent motions called in mechanical systems?
Degrees of freedom
Which component replaces mass in rotational mechanical systems?
Moment of inertia
What is the purpose of drawing a free-body diagram in a mechanical system?
To find the forces acting on the body due to its own motion
What is the relationship between torque and angular velocity in rotational mechanical systems?
Torque is directly proportional to angular velocity
What is the purpose of using superposition in solving mechanical systems?
To activate the other points of motion one at a time
What is backlash in the context of gears?
The loose fit between two meshed gears
According to the information provided, what is the relationship between the rotation of Gear 1, θ1, and Gear 2, θ2?
θ1 is inversely proportional to θ2
If the gears are lossless, what is the relationship between the input torque, T1, and the delivered torque, T2?
T1 is directly proportional to T2
According to the text, how can rotational mechanical impedances be reflected through gear trains?
By multiplying the mechanical impedance by the ratio of the number of teeth
What is the equivalent gear ratio for gear trains?
The product of the individual gear ratios
What is the purpose of using a gear train to implement large gear ratios?
To cascade smaller gear ratios
Which of the following is true about the Laplace transform?
It simplifies the representation of physical systems
What is the Laplace transform of $f(t) = te^{5t}$?
$F(s) = \frac{1}{(s + 5)^2}$
What is the inverse Laplace transform of $F(s) = \frac{10}{(s + 2)(s + 3)^2}$?
$f(t) = 5e^{-2t} + 10te^{-3t} + 40e^{-3t} + 939$
What is the transfer function of the system represented by the block diagram in Figure 2.2?
$G(s) = \frac{b_m s^m + b_{m-1} s^{m-1} + ... + b_0}{a_n s^n + a_{n-1} s^{n-1} + ... + a_0}$
What type of systems can be modeled as transfer functions?
Linear, time-invariant differential equations
Test your knowledge on mechanical systems and their components with this quiz. Learn about the similarities between mechanical and electrical systems and understand the roles of energy-storage elements and energy dissipators.
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