# Dynamic Systems: Mathematical Basics

Source: Saylor

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A question pack on dynamic systems and controls.

Dynamic Systems: Mathematical Basics Q30

All of the following are properties of nonlinear dynamic systems EXCEPT:

A

Linear systems do not satisfy superposition.

B

Linear systems do not satisfy homogeneity.

C

Linear systems have one equilibrium point at origin.

D

Linear systems have many equilibrium points at origin.

Dynamic Systems: Mathematical Basics Q31

Laplace transformations use the ______________ variable?

A

“t”

B

“s”

C

“d”

D

“g”

Dynamic Systems: Mathematical Basics Q32

Poles of a system are obtained by setting the ______________ of the transfer function to zero.

A

Numerator

B

Denominator

C

Natural frequency

D

Gain

Dynamic Systems: Mathematical Basics Q29

Gain of a second order dynamic system exhibits which of the following?

A

How much the system oscillates

B

How fast the system oscillates

C

D

None of the above

Dynamic Systems: Mathematical Basics Q28

How many poles will a second order system have?

A

One

B

Two

C

Three

D

Four

Dynamic Systems: Mathematical Basics Q27

Natural frequency of a second order dynamic system exhibits which of the following?

A

How much the system oscillates

B

How fast the system oscillates

C

D

None of the above

Dynamic Systems: Mathematical Basics Q26

Plots of second order dynamic system exhibit which of the following?

A

Natural frequency

B

Overshoot

C

Gain

D

All of the above

Dynamic Systems: Mathematical Basics Q25

Pole location in dynamic systems is a function of which of the following?

A

Natural frequency

B

Damping ratio

C

Gain

D

None of the above

Dynamic Systems: Mathematical Basics Q24

The damping ratio of a second order dynamic system exhibits which of the following?

A

How much the system oscillates

B

How fast the system oscillates

C

D

None of the above

Dynamic Systems: Mathematical Basics Q23

Which of the following applies to a transfer functions?

A

A transfer function is ratio of transform of input to transform of output.

B

A transfer function is ratio of transform of output to transform of input.

C

Both A and B

D

None of the above

Dynamic Systems: Mathematical Basics Q22

Which of the following can be considered a second order dynamic system?

A

Overdamped

B

Underdamped

C

Undamped

D

All of the above

Dynamic Systems: Mathematical Basics Q21

Which of the following does second order dynamic systems exhibit?

A

Oscillations

B

Overshoot

C

Both A and B

D

None of the above

Dynamic Systems: Mathematical Basics Q20

Which of the following is NOT a characteristic of transfer function?

A

Transfer function applies to nonlinear system.

B

Transfer function applies to stationary systems.

C

During transfer function, computation all initial conditions are assumed as zero.

D

Transfer function describes input‑output dynamics.

Dynamic Systems: Mathematical Basics Q19

Which of the following is NOT a property of linear dynamic systems?

A

Linear systems satisfy superposition.

B

Linear systems satisfy homogeneity.

C

Linear systems have two equilibrium points at origin.

D

Linear systems have one equilibrium point at origin.

Dynamic Systems: Mathematical Basics Q18

A dynamic system at a minimum has ______________ sets of variables.

A

Two

B

Three

C

Four

D

Five

Dynamic Systems: Mathematical Basics Q17

Root Locus of a system has ______________ number of branches compared to open loop poles.

A

More

B

Less

C

The same

D

Zero

Dynamic Systems: Mathematical Basics Q16

Steady state error ______________when the loop gain ______________.

A

Increases, decreases

B

Increases, increases

C

Increases, remains unchanged

D

Remains unchanged, increases

Dynamic Systems: Mathematical Basics Q15

If the response to step input is 0.9 and the error is 0.1, the system is said to have what percent steady state error?

A

6 percent

B

8 percent

C

10 percent

D

12 percent

Dynamic Systems: Mathematical Basics Q14

If the system poles are at the origin, the system is said to have what percent steady state error?

A

1 percent

B

0.05 percent

C

10 percent

D

0 percent

Dynamic Systems: Mathematical Basics Q13

Root Locus of a first order system has how many branches?

A

0

B

1

C

2

D

3

Dynamic Systems: Mathematical Basics Q12

Root Locus of a second order system has how many branches?

A

0

B

1

C

2

D

3

Dynamic Systems: Mathematical Basics Q10

The distance of poles from the origin of a dynamic system gives which of the following?

A

Frequency of oscillations

B

Reciprocal of time constant

C

Undamped natural frequency

D

None of the above

Dynamic Systems: Mathematical Basics Q9

The horizontal location of poles of a dynamic system gives which of the following?

A

Frequency of oscillations

B

Reciprocal of time constant

C

Undamped natural frequency

D

None of the above

Dynamic Systems: Mathematical Basics Q8

The vertical location of poles of a dynamic system gives which of the following?

A

Frequency of oscillations

B

Reciprocal of time constant

C

Undamped natural frequency

D

None of the above

Dynamic Systems: Mathematical Basics Q7

To evaluate steady state error, which of the following input signal is commonly used?

A

Impulse

B

Step

C

Ramp

D

Random

Dynamic Systems: Mathematical Basics Q5

Where does Root Locus begin?

A

At open loop zeros

B

At closed loop zeros

C

At open loop poles

D

At closed loop poles

Dynamic Systems: Mathematical Basics Q5

Where does Root Locus end?

A

At open loop zeros

B

At closed loop zeros

C

At open loop poles

D

At closed loop poles

Dynamic Systems: Mathematical Basics Q4

Which of the following best describes steady state error?

A

Difference between input and measured varying output

B

Difference between input and measured constant output

C

Difference between measured constant input and measured varying output

D

None of the above

Dynamic Systems: Mathematical Basics Q3

Steady state error is also known as ______________ error.

A

AC

B

DC

C

On‑Off

D

Integral

Dynamic Systems: Mathematical Basics Q2

For a stable integral control system, what is the steady state error?

A

0.1

B

0.01

C

0

D

1

Dynamic Systems: Mathematical Basics Q1

Z‑transformation is based on which of the following?

A

Laplace

B

State‑space

C

Both A and B

D

None of the above

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