Simple Harmonic Motion

Simple Harmonic Motion

1. Oscillation

   • An object that moves repeatedly one way then in the opposite direction through its equilibrium position with a continually changing displacement - e.g. a child on a swing.
   • Key Terms
     • Amplitude
       • Maximum displacement from equilibrium.
     • Time Period
       • Time for one cycle in which the object passes through the same position twice in the same direction.
     • Frequency
       • Number of cycles per second made by an oscillating object.
     • Phase Difference
       • Fraction of a cycle difference between two things oscillating.

2. Acceleration is always proportional to and in the opposite direction to the displacement.

3. Factors that can affect frequency of oscillation of a loaded spring

   • Adding extra mass
   • Using weaker springs

4. For a simple pendulum, if the angle of displacement is less than 10 degrees, than sin of the angle can be taken to be displacement divided by length.

5. Free Oscillations

   • An object that oscillates with constant amplitude due to no friction acting on it. If friction was present, the amplitude of the oscillations would decrease to an eventual halt.

6. Damping

   • Light
     • Occurs where time period is independent of amplitude so each cycle takes the same amount of time however the amplitude consistently decreases with each cycle.
   • Heavy
     • Occurs when the damping is so strong that oscillations cease however the object takes much longer than critical damping to return to equilibrium.
   • Critical
     • When a system has been damped just enough to stop oscillating after it has been displaced and released and the system returns to equilibrium in the shortest time without overshooting.

7. Forced Vibrations

   • If a force is applied at regular intervals, its known as periodic force.
   • A system that does not have periodic force applied is at its natural frequency.
   • When a periodic force is applied to a system, it undergoes forced vibrations.

8. Resonance in textbook terms

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