Piecewise function plots weird when given expression with symbol vs writing it explicitly

Asked Oct 24 '15 at 10:19

Active Oct 24 '15 at 10:19

Viewed 35 times

The only difference is that in the second snippet the expression is written out explicitly.

displacement = (Sin[x - Pi/2 - t] + 1)/2

This doesn't work:

Manipulate[
 Plot[
  {
   Piecewise[{{displacement, t <= x <= t + 2 Pi}}, 0]
   },
  {x, 0, 20},
  PlotRange -> All
  ],
 {t, 0, 20}
 ]

but this works:

Manipulate[
 Plot[
  {
   Piecewise[{{(Sin[x - Pi/2 - t] + 1)/2, t <= x <= t + 2 Pi}}, 0]
   },
  {x, 0, 20},
  PlotRange -> All
  ],
 {t, 0, 20}
 ]

asked Oct 24 '15 at 10:19

user

1

Add Evaluated -> True to the Plot[] and try again. – J. M.'s missing motivation Oct 24 '15 at 10:38
@J.M. Doesn't work. – user Oct 24 '15 at 10:45
Ah, I see what's happening: try looking at the result of Manipulate[Table[displacement, {x, 0, 2}], {t, 0, 20}]. – J. M.'s missing motivation Oct 24 '15 at 10:51
@J.M. Yeah it outputs {1/2 (1 - Cos[t]), 1/2 (1 - Cos[1 - t]), 1/2 (1 - Cos[2 - t])} and the "t"s aren't changing. – user Oct 24 '15 at 11:05
So, you now understand what happened to your original example? – J. M.'s missing motivation Oct 24 '15 at 11:16
@J.M. I don't. What is the difference between writing the expression explicitly and assigning the value to a symbol and using that? – user Oct 24 '15 at 16:55
You saw what happened with Table[]. That is what's happening to Plot[] too, which of course cannot plot anything with a dangling symbol. – J. M.'s missing motivation Oct 24 '15 at 17:07
1

@J.M. Finally I get it. This works. Manipulate[ Plot[ { Piecewise[{{(displacement /. t -> time), time <= x <= time + 2 Pi}}, 0] }, {x, 0, 20}, PlotRange -> All, Evaluated -> True ], {time, 0, 20} ] Have I understood correctly that the Manipulate function replaces all occurrences of t before evaluating the Piecewise. So because it doesn't contain t before evaluation it is left dangling. – user Oct 24 '15 at 17:25
More or less, yes. :) Consider writing an answer to your own question. – J. M.'s missing motivation Oct 24 '15 at 17:29

0 Answers0