Force vibration and resonance

Question 1

What is a periodic force?

Answer 1

A force that varies regularly in magnitude with a definite time period.

Question 2

What are forced vibrations?

Answer 2

Vibrations (oscillations) of a system subjected to an external periodic force.

Question 3

What is the natural frequency?

Answer 3

The frequency of free oscillations of an oscillating system.

Question 4

What is the resonant frequency?

Answer 4

The frequency of an oscillating system in resonance.

Question 5

When increasing the periodic force of an oscillating system. As the applied frequency increases:

Answer 5

• The amplitude of oscillation of the system increasese until it reaches a maximumum amplitude at a particular frequency, and then decreases again.
• The phase difference between the displacement and the periodic force increases from 0 to π/2 at the maximum amplitude, then decreases from π/2 to π as the frequency increases further.

Question 6

When the system is oscillating at the maximum velocity:

Answer 6

• The phase difference between the displacement and the period force is π/2.
• The periodic force is in phase with the velocity of the oscillating system, and the system is in resonance.

Question 7

For a lightly damped system:

Answer 7

• The larger the max amplitude becomes at resonance
• The closer the resonant frequency is to the natural frequency of the system.
• So when the dampening is lighter, the resonance curve is sharper.

Question 8

As the applied frequency become higher than the resonant frequency:

Answer 8

• The amplitude of oscillations decreases more and more
• The phase difference between the displacement and the periodic force increases from π/2 until the displacement is π radians out of phase with the periodic force.

Question 9

For an oscillating system with little or no damnping, at resonance:

Answer 9

The applied frequency of the period force = the natural frequency of the system