Oscillations

Oscillations

1. Pendulums

   • Restoring force - The force that pulls the pendulum bob back to the centre line
   • The resultant force always acts opposite to the direction of motion
   • Ek max occurs when the pendulum is passing the centre line
   • Eg max occurs when the pendulum is at its maxima
   • The frequency and the period don't depend on the amplitude

2. Damping

   • Graphs
   • Light Damping is a small damping force, where the amplitude reduces over a long time
   • Heavy Damping is caused by a large force, reducing oscillations over a short period of time
   • Critical Damping stops oscillations instantly, without the wave oscillating again
   • Over damping is the same as critical damping, however the oscillation takes longer to die out
   • A heavily damped system creates smaller peaks when a system is resonating

3. Experiments

   • SHM Experiment with a spring
   • SHM Experiment with a pendulum

4. Formulae

   • max a = (w)^2 x A
   • v = w sqrt(A^2 - x^2)
   • x = Acos(wt)

5. SHM

   • An oscillation in which the acceleration of an object is directly proportional to its displacement, and the force causes acceleration towards the midpoint
   • The displacement is the distance from the midpoint
   • Free vibrations are where there is no energy transfer to or from the surroundings
     • When a spring acts under free vibrations, it oscillates at its natural Frequency
   • Forced vibrations occur when there is an external driving force caused by a periodic external force
   • When the Natural Frequency = Driving Frequency, resonance occurs
     • When an object is resonating, its ocsillations increase in amplitude as more and more energy is gained

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