SHM - Forced vibrations & resonance *was missed*

Question 1

What is a periodic force?

Answer 1

• force applied at regular intervals
• e.g. pushing swing

Question 2

What is a systems natural frequency?

Answer 2

• when a system oscillates without a periodic force

Question 3

What are forced vibrations? What does the response of the system depend on?

Answer 3

• when a periodic force is applied, the response depends on the fequency of the periodic force
• the system undergoes forced vibrations, when a periodic force is applied to it

Question 4

What happens as applied frequency increases?

Answer 4

• amplitude of oscillations increases until it reaches a maxiumum amplitude at a paticular freq, then decreases again
• the phase difference between the displacement and the periodic force increases from zero to 1/2π at the max amplitude, then from 1/2π to π as the freq increases further

Question 5

What is the phase difference between the displacement and the periodic force at max amplitude?

Answer 5

• 1/2π

Question 6

What is resonance?

Answer 6

• when the periodic force is exactly in phase with the velocity of the oscillating system (1/2 π phase difference)
• forced vibration frequency = natural frequency of systyem
• maximum transfer of energy
• no damping
• max amplitude

Question 7

What is the resonant frequency?

Answer 7

• the freq at the maximum amplite is the resonant frequency

Question 8

What affect does damping have on resonance?

Answer 8

• the lighter the damping,
  
  • the larger the maximum amplitude becomes at resonance
  • the closer the resonant freq is to the natural freq of the system
• no damping at resonance:
  
  • ​the applied freq of the periodic force = the natural freq of the system

Question 9

What happens as the applied frequency becomes larger than the resonant frequency of the mass-spring system?

Answer 9

• amplitude decrease more and more
• phase difference between the displace and the periodic force increases from 1/2π until the displace is π radiants out phase with the periodic force

Question 10

What causes damping in a simple pendulum? What is the affect of adding mass?

Answer 10

• damping caused by air resistance
• given same area
  
  • bob with more mass has more kinetic energy at the same amplitude
  • smaller fraction of energy removed per oscillation
  • # intertia of heavier bob greater