Swinging Spiral Pendulum

About oscillations of spirals in sine rythm.

Swinging Spiral Pendulum:
For the construction of a spiral pendulum we need to calculate its actual length.
First we define the minimal length and the amplitude of the spiral. With this values we calculate the medium length:

#declare Amplitude = 0.60;
#declare Minimal_Length   = 0.80;
#declare Middle_Length    = Amplitude + Minimal_Length;

//---------------------------------------------- time ----------------------
#declare Time_test = 0.25; // 0.25/0.75 shows maximum/minimal extension!!!

#declare Spiral_Length = Middle_Length+Amplitude*sin((clock+Time_test)*2*pi);
//------------------------------------------------------ -------------------
  

scene description for POV-Ray:
"spiral0.ini" and
"spiral0.pov"

The Spiral made with a While Loop:

#declare Spiral  =  //--------------------------------- the spiral
union{
 #local N_per_Rev = 500;   // Number of Elements per revolution
 #local N_of_Rev  = 8.00;  // Total number of revolutions
 #local H_per_Ref = Sp_Length / N_of_Rev;// Height per revolution
 #local Nr = 0;                          // start loop
 #while (Nr< N_per_Rev*N_of_Rev)
   sphere{ <0,0,0>,0.025
           translate<0.25, -Nr*H_per_Ref/N_per_Rev, 0>
           rotate<0,  Nr * 360/N_per_Rev,0/gt;

           texture{ Chrome_Metal
                    finish {diffuse 0.9 phong 1}}
         }
 #local Nr = Nr + 1;    // next Nr
 #end // --------------------------------- end of loop

  sphere {<0,0,0>, 0.4
          translate<0,-Nr*H_per_Ref/N_per_Rev-0.2,0>
          texture{ pigment{color rgb<1,0.65,0>}
                   finish {diffuse 0.9 phong 1}}
        }
} // end of union  -------------------------------- end of spiral


object { Spiral  translate< 0.0,2.42,0>}
//------------------------------------------------