Math 224-01: Differential Equations: Reading Homework 4.2

1. Beats and Resonanace : what system are we considering in this section? what solutions do we have for this?
   
   1. Free Oscillations : what's a harmonic oscillator?
      
      1. Point : what general solution is given for the harmonic oscillator?
         
      2. Point : what do we call the motion of a harmonic oscillator?
         
   2. Damped, Free Oscillations : what happens when we add damping to the oscillator?
      
      1. Point : what are the three cases for the damped oscillator? which oscillate? which decay the fastest?
         
   3. Forced Oscillations : what is resonance?
      
      1. Point : what differential equation produces resonance? what solutions do we find when a system is in resonance?
         
      2. Point : what are beats? when do we see them? what is the beat frequency?