swing of the pendulum

Questions
1

I would like to visualize a swing of the pendulum. I want to write a function springmass[z, nzigzag], which will draw the spring (line) and the swinging weight (rectangle) for an default total length z and a quantity of spring coils (nzigzag).

I should animate the motion with exactly this line:

Animate[Graphics[springmass[5 + Sin[?], 23],PlotRange -> {-9, 0}], {?, 0, 2 ?}]

That’s what I found on the internet:

With[{min = .4}, 
  vspring[a0_, y10_, y20_] := 
    Module[{a = a0, y1 = y10 + min, y2 = y20, n = 100}, 
      h = (y2 - y1)/n; 
      yvalues = Table[k, {k, y1, y2, h}]; 
      xvalues = Table[a Sin[(m ?)/2], {m, 0, n}]; 
      Line[Transpose[{xvalues, yvalues}]]]]

and

With[{size = .2}, 
  Animate[
    Graphics[{
      vspring[0.2, 0, 2 Sin[y]], 
      Red, Thickness[5 size], Line[{{-.5 size, 2 Sin[y]}, {.5 size, 2 Sin[y]}}]}, 
      PlotRange -> {{-size, size}, {-2.2 , 2 size}}], 
    {y, -?, 0, 0.1}]]

But I have one question. I should use this line:

Animate[Graphics[springmass[5 + Sin[?], 23],PlotRange -> {-9, 0}], {?, 0, 2 ?}]

The vspring function of the internet code have 3 parameters and the “required” line (the function springmass) have 2 parameters. How can I change that?

Thanks for your help!!!

2

It is best to give your variables some plain understandable names. Like in you function:( this is a spring with diameter and start and endpoint)

springmass[start_: 0, end_, diameter_] := 
 Module[{a = diameter, y1 = start, y2 = end, n = 100}, h = (y2 - y1)/n;
  yvalues = Table[k, {k, y1, y2, h}];
  xvalues = Table[a Sin[(m \[Pi])/2], {m, 0, n}];
  Line[Transpose[{xvalues, yvalues}]]]

This will then make a simple manipulate:

Manipulate[With[{size = .2},
  Animate[
   Graphics[{
     vspring[diameter, start, 2 Sin[y]],
     Red, Thickness[5 size], 
     Line[{{-.5 size, 2 Sin[y]}, {.5 size, 2 Sin[y]}}]}, 
    PlotRange -> {{-size, size}, {-2.2, 2 size}}, Axes -> True, 
    ImageSize -> Small],
   {y, -\[Pi], 0, 0.1}]],
 {{diameter, .2}, .05, 1},
 {{start, 0}, -1, 1}]

spring.gif

your function springs eliminates the strapping and considers it to be zero:springmass[start_: 0, end_, diameter_] :=
Module[{a = diameter, y1 = start, y2 = end, n = 100}, h = (y2 - y1)/n;
yvalues = Table[k, {k, y1, y2, h}];
xvalues = Table[a Sin[(m [Pi])/2], {m, 0, n}];
Line[Transpose[{xvalues, yvalues}]]]
This way no need for a third variable since the default value _:0 will be chosen.

Animate[Graphics[springmass[5 + Sin[\[CurlyPhi]], 1], 
  PlotRange -> {{-5, 5}, {0, 7}}, Axes -> True], {\[CurlyPhi], 0, 
  2 \[Pi]}]

spring2.gif

It is better to explain the question more in detail since it was hard to guess what this was all about. But this will hopefully be of help.
[1]: /c/portal/getImageAttachment?filename=spring.gif&userId=68637
[2]: /c/portal/getImageAttachment?filename=spring2.gif&userId=68637

3

It is best to give your variables some plain understandable names. Like in you function:( this is a spring with diameter and start and endpoint)

springmass[start_: 0, end_, diameter_] := 
 Module[{a = diameter, y1 = start, y2 = end, n = 100}, h = (y2 - y1)/n;
  yvalues = Table[k, {k, y1, y2, h}];
  xvalues = Table[a Sin[(m \[Pi])/2], {m, 0, n}];
  Line[Transpose[{xvalues, yvalues}]]]

This will then make a simple manipulate:

Manipulate[With[{size = .2},
  Animate[
   Graphics[{
     vspring[diameter, start, 2 Sin[y]],
     Red, Thickness[5 size], 
     Line[{{-.5 size, 2 Sin[y]}, {.5 size, 2 Sin[y]}}]}, 
    PlotRange -> {{-size, size}, {-2.2, 2 size}}, Axes -> True, 
    ImageSize -> Small],
   {y, -\[Pi], 0, 0.1}]],
 {{diameter, .2}, .05, 1},
 {{start, 0}, -1, 1}]

spring.gif

your function springs eliminates the strapping and considers it to be zero:springmass[start_: 0, end_, diameter_] :=
Module[{a = diameter, y1 = start, y2 = end, n = 100}, h = (y2 - y1)/n;
yvalues = Table[k, {k, y1, y2, h}];
xvalues = Table[a Sin[(m [Pi])/2], {m, 0, n}];
Line[Transpose[{xvalues, yvalues}]]]
This way no need for a third variable since the default value _:0 will be chosen.

Animate[Graphics[springmass[5 + Sin[\[CurlyPhi]], 1], 
  PlotRange -> {{-5, 5}, {0, 7}}, Axes -> True], {\[CurlyPhi], 0, 
  2 \[Pi]}]

spring2.gif

It is better to explain the question more in detail since it was hard to guess what this was all about. But this will hopefully be of help.
[1]: /c/portal/getImageAttachment?filename=spring.gif&userId=68637
[2]: /c/portal/getImageAttachment?filename=spring2.gif&userId=68637