Do and study the following examples in Maple. These are important in Chapter 5 when we study vibrating systems such as the spring-mass apparatus and electronic circuits. Type these verbatim into a Maple session. Do NOT merely copy and paste them into a Maple session.

1. Examples of simple harmonic motion (constant amplitude oscillation):
   1. x := t –> 6 * cos(4*t) ;
      plot ( x(t), t = 0.0 .. 2*Pi, thickness=4, color="Blue" ) ;
      the symbol –> is the minus sign followed immediately by a greater than symbol (no space between them)

   2. x := t –> 6 * sin(4*t) ;
      plot ( x(t), t = 0.0 .. 2*Pi, thickness=4, color="Red" ) ;

   3. x := t –> 3 * cos(2*t) – 4 * sin(2*t) ;
      plot ( x(t), t = 0.0 .. 3*Pi ) ;

2. Example of underdamped motion (decaying oscillation):
   1. x := t –> exp(–t) * ( 3 * cos(2*t) – 4 * sin(2*t) ) ;
      plot ( x(t), t = 0.0 .. 2*Pi, thickness=4, color="Green" ) ;

3. Examples of critically damped motion:
   1. x := t –> exp(–t/2) * ( 4 – 5*t ) ;
      plot ( x(t), t = 0.0 .. 20.0, thickness=4, color="Magenta" ) ;

   2. x := t –> exp(–t/2) * ( 4 + 5*t ) ;
      plot ( x(t), t = 0.0 .. 20.0, thickness=4, color="Purple" ) ;

4. Example of overdamped motion:
   1. x := t –> 6*exp(–t) – 5*exp(–2*t) ) ;
      plot ( x(t), t = 0.0 .. 6.0, thickness=4, color="Cyan" ) ;

5. Examples of undamped motion (mixed modes):
   1. x := t –> cos(t) – cos(2*t) ) ;
      plot ( x(t), t = 0.0 .. 4*Pi, thickness=4, color="Blue" ) ;

   2. x := t –> cos(t) – 3*cos(2*t) ) ;
      plot ( x(t), t = 0.0 .. 4*Pi, thickness=4, color="Navy" ) ;

6. Examples of pure resonance (unbounded oscillation):
   1. x := t –> t*cos(t) ;
      plot ( x(t), t = 0.0 .. 6*Pi, thickness=4, color="Red" ) ;

   2. x := t –> t*cos(2*t) ;
      plot ( x(t), t = 0.0 .. 6*Pi, thickness=4, color="Green" ) ;

   3. x := t –> 3*sin(2*t) + t*cos(2*t) ;
      plot ( x(t), t = 0.0 .. 6*Pi, thickness=4, color="Blue" ) ;

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