Math 224-01: Differential Equations: Reading Homework 4.2

1. Beats and Resonance : what interpretations does the second-order linear constant-coefficient (forced) ODE we have been considering have? when are all solutions to this ODE known?
   
   1. Free Oscillations : what is the harmonic oscillator ODE? what are solutions to this? what parameters describe its oscillations?
      
   2. Damped Oscillations : how is the ODE for a damped oscillator different from that for the harmonic oscillator?
      
      1. cases : what are the three cases for solutions to the damped oscillator? what are the solutions obtained in each case?
         
   3. Forced Oscillations : what ODE do we consider for forced oscillations?
      
      1. pure resonance : when does pure resonance occur? what happens to solutions in this case?
         
      2. beats : when do beats occur? what solutions do we have in this case?