# Dynamic Systems: Mathematical Basics

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A question pack on dynamic systems and controls.

This content is licensed under the Creative Commons Attribution 3.0 Unported License.

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

Linear systems do not satisfy superposition.

Linear systems do not satisfy homogeneity.

Linear systems have one equilibrium point at origin.

Linear systems have many equilibrium points at origin.

Laplace transformations use the ______________ variable?

“t”

“s”

“d”

“g”

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

Numerator

Denominator

Natural frequency

Gain

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

How much the system oscillates

How fast the system oscillates

Size of steady state response

None of the above

How many poles will a second order system have?

One

Two

Three

Four

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

How much the system oscillates

How fast the system oscillates

Size of steady state response

None of the above

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

Natural frequency

Overshoot

Gain

All of the above

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

Natural frequency

Damping ratio

Gain

None of the above

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

How much the system oscillates

How fast the system oscillates

Size of steady state response

None of the above

Which of the following applies to a transfer functions?

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

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

Both A and B

None of the above

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

Overdamped

Underdamped

Undamped

All of the above

Which of the following does second order dynamic systems exhibit?

Oscillations

Overshoot

Both A and B

None of the above

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

Transfer function applies to nonlinear system.

Transfer function applies to stationary systems.

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

Transfer function describes input‑output dynamics.

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

Linear systems satisfy superposition.

Linear systems satisfy homogeneity.

Linear systems have two equilibrium points at origin.

Linear systems have one equilibrium point at origin.

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

Two

Three

Four

Five

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

More

Less

The same

Zero

Steady state error ______________when the loop gain ______________.

Increases, decreases

Increases, increases

Increases, remains unchanged

Remains unchanged, increases

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?

6 percent

8 percent

10 percent

12 percent

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

1 percent

0.05 percent

10 percent

0 percent

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

0

1

2

3

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

0

1

2

3

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

Frequency of oscillations

Reciprocal of time constant

Undamped natural frequency

None of the above

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

Frequency of oscillations

Reciprocal of time constant

Undamped natural frequency

None of the above

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

Frequency of oscillations

Reciprocal of time constant

Undamped natural frequency

None of the above

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

Impulse

Step

Ramp

Random

Where does Root Locus begin?

At open loop zeros

At closed loop zeros

At open loop poles

At closed loop poles

Where does Root Locus end?

At open loop zeros

At closed loop zeros

At open loop poles

At closed loop poles

Which of the following best describes steady state error?

Difference between input and measured varying output

Difference between input and measured constant output

Difference between measured constant input and measured varying output

None of the above

Steady state error is also known as ______________ error.

AC

DC

On‑Off

Integral

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

0.1

0.01

0

1

Z‑transformation is based on which of the following?

Laplace

State‑space

Both A and B

None of the above

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