Vibrations Learning Quizzes for Engineering Mechanics MEng Students

Question 1

In a single-degree-of-freedom system with damping, how does the damping ratio ζ influence the system's response to a transient disturbance?

Accepted Answer

Damping extends the system's settling time and reduces its overshoot.

Answer

Damping shortens the system's settling time and increases its overshoot.

Answer

Damping has no impact on the system's settling time or overshoot.

Question 2

In a single-degree-of-freedom system, what frequency of the applied harmonic force will cause the system to resonate, given its natural frequency of ωn?

Accepted Answer

ω = ωn

Answer

ω = 0

Answer

ω = 2ωn

Question 3

Specify which of the following is not a distinguishing attribute of a single-degree-of-freedom system:

Accepted Answer

Exhibits non-linear damping behavior

Answer

Possesses a singular natural frequency

Answer

Undergoes undamped motion

Answer

Maintains constant mass

Question 4

In the context of free vibration, the damping ratio is responsible for determining the:

Accepted Answer

Rate of decay

Answer

Frequency of vibration

Answer

Amplitude of vibration

Answer

Phase angle of vibration

Question 5

Identify the type of forced vibration characterized by the following:

Accepted Answer

Harmonic vibration

Answer

Transient vibration

Answer

Free vibration

Answer

Damped vibration

Question 6

Under which condition does the amplitude of forced vibration reach its maximum value?

Accepted Answer

When the frequency of the external force matches the natural frequency

Answer

When the frequency of the external force exceeds the natural frequency

Answer

When the frequency of the external force is lower than the natural frequency

Answer

When the damping ratio is low

Question 7

Which of the following is NOT a viable method to minimize vibration amplitude?

Accepted Answer

Applying an external force

Answer

Increasing damping

Answer

Altering the natural frequency

Answer

Utilizing vibration isolation

Question 8

The logarithmic decrement of a damped system provides a measure of its:

Accepted Answer

Rate of amplitude decay

Answer

Frequency of vibration

Answer

Damping ratio

Answer

Stiffness of the system

Question 9

A single-degree-of-freedom system has a natural frequency of 10 Hz and a damping ratio of 0.2. What is its damped natural frequency?

Accepted Answer

9.6 Hz

Answer

8 Hz

Answer

10 Hz

Answer

12 Hz

Question 10

The natural frequency of an undamped single-degree-of-freedom system is given by:

Accepted Answer

√(k/m)

Answer

k/m

Answer

m/k

Answer

√(m/k)

Question 11

Which characteristic is NOT associated with forced vibrations?

Accepted Answer

Damping

Answer

Steady-state response

Answer

Transient response

Answer

Resonance

Question 12

The condition for resonance in a single-degree-of-freedom system is:

Accepted Answer

ω = ωn

Answer

ω > ωn

Answer

ω < ωn

Answer

ω = 0

Question 13

The logarithmic decrement of a damped system represents:

Accepted Answer

The natural logarithm of the ratio of successive amplitudes

Answer

The damping ratio divided by the natural frequency

Answer

The change in amplitude over one period

Answer

The time it takes for the amplitude to decrease by half

Question 14

Which of the following is NOT a passive damping mechanism in vibrating systems?

Accepted Answer

Active control

Answer

Viscous damping

Answer

Coulomb damping

Answer

Structural damping

Question 15

Define vibration transmissibility and describe how it changes with frequency and damping ratio. Include a graph to illustrate your explanation.

Accepted Answer

Vibration transmissibility is the ratio of the amplitude of the transmitted force to the amplitude of the applied force.

Answer

Transmissibility is independent of both frequency and damping ratio.

Answer

Transmissibility is always greater than 1.

Question 16

A mass-spring system is subjected to a harmonic force. The system's natural frequency is 5 Hz, and the forcing frequency is 10 Hz. What is the expected behavior of the system?

Accepted Answer

The system will exhibit resonance, leading to large amplitude oscillations.

Answer

The system will oscillate at a frequency of 10 Hz with a small amplitude.

Answer

The system will oscillate at a frequency of 5 Hz with a large amplitude.

Question 17

A single-degree-of-freedom system has a mass of 10 kg and a spring stiffness of 1000 N/m. What is the natural frequency of the system?

Accepted Answer

3.16 Hz

Answer

10 Hz

Answer

100 Hz

Answer

1 Hz

Question 18

A damped vibration system experiences a decrease in amplitude over time. What is the primary factor responsible for this damping?

Accepted Answer

Energy dissipation due to friction or other resistance forces.

Answer

Increasing the amplitude of the forcing function.

Answer

Changes in the system's natural frequency.

Question 19

A vibrating system is described by the equation x(t) = A * sin(ωt + φ). What does the term 'φ' represent?

Accepted Answer

The phase angle, indicating the initial position of the system.

Answer

The natural frequency of the system.

Answer

The amplitude of vibration.

Question 20

Which of the following scenarios would NOT result in an increase in the natural frequency of a mass-spring system?

Accepted Answer

Increasing the mass of the system.

Answer

Increasing the stiffness of the spring.

Answer

Using a spring with a higher spring constant.

Answer

Decreasing the mass of the system.

Question 21

A vibrating system is said to be critically damped. What is the characteristic behavior of such a system?

Accepted Answer

It returns to its equilibrium position as quickly as possible without oscillating.

Answer

It oscillates with a decreasing amplitude.

Answer

It oscillates with a constant amplitude.

Question 22

A car traveling on a bumpy road experiences vibrations. What type of vibration is this an example of?

Accepted Answer

Forced vibration

Answer

Resonant vibration

Answer

Free vibration

Answer

Damped vibration

Question 23

A vibrating system is subjected to a periodic force. What is the relationship between the forcing frequency and the amplitude of vibration when the system is near resonance?

Accepted Answer

The amplitude of vibration increases significantly as the forcing frequency approaches the natural frequency.

Answer

The amplitude remains constant regardless of the forcing frequency.

Question 24

What is the main purpose of adding damping to a vibrating system?

Accepted Answer

To reduce the amplitude of vibrations and prevent excessive oscillations.

Answer

To increase the natural frequency of the system.

Answer

To create a more comfortable riding experience.