Vibrations

Vibrations

1. Damping

   • energy is lost to the surroundings
   • systems are damped to minimise the effect of resonance
   • reduces the amplitude of the oscillation over time
     • heavier damping leads to quicker amplitude reduction
   • critical damping
     • reduces amplitude in shortest possible time
   • affects resonance
     • lightly damped systems
       • very sharp resonance peak
         • amplitude increases dramatically when driving frequency is close to natural frequency
     • heavily damped systems
       • flatter resonance peak
         • amplitude doesn't increase very much near natural frequency

2. natural frequency

   • free vibrations
   • no energy transfer to or from surroudings

3. resonance

   • phase difference between the driver and oscillator is 90 degrees
   • driving frequency equals the natural frequency
     • as driving frequency approaches natural frequency the amplitude increases
       • as driving frequency goes beyond natural frequency, the amplitude decreases
   • amplitude at maximum when system is resonating

4. forced vibrations

   • external driving force causes system to vibrate at driving frequency