Free and Forced vibrations

Question 1

What is resonance?

Answer 1

When the frequency of the driving force matches the natural frequency of the oscillating system, the amplitude of the resulting oscillations increases significantly

Question 2

What’s the phase difference between driver and oscillator at resonance?

Answer 2

90 degrees

Question 3

What are free vibrations?

Answer 3

• No transfer of energy to or from the surroundings
• Realistically this never happens because energy is lost to surroundings
• But a spring vibrating in air is called a free vibration

Question 4

What are forced vibrations?

Answer 4

• The system is forced to vibrate by a periodic external force
• The frequency of this force is called the driving frequency

Question 5

What happens if the driving frequency is much less than the natural frequency?

Answer 5

The driver and the oscillator are in phase

Question 6

What happens if the driving frequency is much more than the natural frequency?

Answer 6

The oscillator and driver will be completely out of phase (in antiphase) because the oscillator won’t be able to keep up with the driver

Question 7

What are the 3 different types of damping?

Answer 7

Under damping: The oscillation slowly dies away (exponential decay)
Over damping: The displaced object takes a long time to return to the equilibrium position and does not oscillate
Critical damping: Just enough to stop the oscillation as quickly as possible often about T/4

Question 8

What is damping?

Answer 8

Reduces the amplitude of resonance vibrations

Question 9

What happens as damping is increased?

Answer 9

• The amplitude of resonance vibrations decrease, meaning the peak of the curve lowers
• The resonance peakbroadens
• The resonance peak moves slightly to theleftof the natural frequency when heavily damped