Forced Vibrations And Resonance

Question 1

What defines free vibrations?

Answer 1

Free vibrations are those that occur in a system with no energy loss.

Question 2

What is the phase relationship between driver and responder when the driving frequency is: A-Much less than the natural frequency; B-Equal to the natural frequency; and C-Much more than the natural frequency?

Answer 2

A-0 phase difference.
B-π/2 phase difference.
C-π phase difference.

Question 3

Define resonance.

Answer 3

Resonance is when the driver and responder have a constant phase difference of π/2 and the driving frequency is equal or close to the natural frequency of the system, and as such maximum energy is transferred from the driver to the responder.

Question 4

What is damping?

Answer 4

Damping is the loss of energy from a system moving with SHM.

Question 5

What describes a system that is ‘lightly’ damped?

Answer 5

The system will take many oscillations for the amplitude to fall to 0.

Question 6

What describes a system that is ‘heavily’ damped?

Answer 6

A system where oscillations stop after only a few oscillations.

Question 7

What describes a system that is ‘over’ damped?

Answer 7

Oscillations never begin and the object simply returns to equilibrium.

Question 8

What describes a system that is ‘critically’ damped?

Answer 8

The object returns to the equilibrium in less than 1/4 of the period.

Question 9

What defines the natural frequency of a system.

Answer 9

The natural frequency of a system is that frequency which the system oscillates at if displaced and then released.