Simple Harmonic Motion

Simple Harmonic Motion

1. Oscillations

   • lowest point
     • equilibrium
   • full cycle
     • maximum height on one side to maximum height on the other
   • displacement
     • decreases as it returns to equilibrium
     • increases as it moves away from equilibrium
   • amplitude
     • maximum displacement of oscillating object form equilibrium
   • time period
     • time for one complete cycle of oscillations
   • frequency
     • number of cycles per second

2. acceleration

   • proportional to the displacement
   • in opposite direction to the displacement

3. resultant force

   • acts towards equilibirum
   • restoring force
     • makes object exchange PE to KE
       • as object moves towards midpoint
         • restoring force does work on object
           • transfers PE to KE
       • as object moves away from midpoint
         • KE transferred to PE
       • at midpoint
         • PE is zero
         • KE is maxiumum
       • at max displacement
         • KE is zero
         • PE is maxiumum

4. Free oscillations

   • constant amplitude
     • no friction
       • if friction present
         • amplitude would gradually decrease
           • total energy is reduced
     • no energy transfer

5. Damped oscillations

   • dissipative forces
     • forces causing amplitude to deacrese
       • air resistance
       • friction
     • dissipate the energy of the system to the surroundings as thermal energy
   • light damping
     • amplitude gradually decreases
       • reduced by the same fraction each cycle
   • critical damping
     • oscillating object returns to equilibrium in the shortest possible time without overshooting
   • heavy damping
     • the displaced object returns to equilibrium much more slowly than if it were critically damped
     • no oscillating motion occurs

6. Forced oscillations

   • periodic force is applied to an oscillating system
     • response depends on the frequency of the periodic force
     • force applied at regular intervals
   • as applied frequency approaches natural frequency
     • amplitude increases
     • phase difference between displacement and periodic force increases from 0 to Pi/2 at natural frequency

7. natural frequency

   • system oscillates without a periodic force being applied

8. Resonance

   • applied frequency is equal to the natural frequency
   • amplitude becomes very large
     • largest when applied frequency equals natural frequency
   • phase difference between displacement and periodic force is Pi/2
     • periodic force is in phase with the velocity

9. frequency and period independent of amplitude