Amplitude of a Sinus, Simple question

Question

I have a rather simple question. I would like to find the Amplitude of a Sinus using mathematica:

w=10;    
5*Sin[w*t-2]

The Amplitude is obviously 5.

Now, what I tried was to first convert the Sinus into Exponential Form:

TrigToExp[5*Sin[w*t-2]]

And then to Take the Norm:

TrigToExp[5*Sin[w*t-2]] //Norm

but it does not work... Thanks, for any help!

It doesn't return what you expect because MMA doesn't know whether t and w are real or not. Wrap the whole lot in ComplexExpand and you'll get your answer: 5 Abs[Sin[2 - t w]] — Quantum_Oli, Oct 17 '16 at 12:54
@Quantum_Oil How do want to implement it ? I tried it, but it does not work... — henry, Oct 17 '16 at 19:13
@Michael E2 I just wanted something simpler than was presented before. But yes, why not? Maximize is even better because it gives a symbolic answer. — Dr. Wolfgang Hintze, Oct 18 '16 at 17:32

score 11 · Answer 1 · answered Oct 17 '16 at 12:55

11

One way is to use Interval.

range = 5*Sin[w*t - 2] /. t -> Interval[{-Infinity, Infinity}]
amplitude = Max[range]
(*
  Interval[{-5, 5}]
  5  
*)

Or, this would take into account a translation:

amplitude = (Max[range] - Min[range])/2
(* 5  *)

answered Oct 17 '16 at 12:55

Michael E2

thanks a lot!... but why can I not simply convert it to a complex function and take the norm ? I don't see why it would not work ? – henry Oct 18 '16 at 11:23
@DoHe Converting a function to an equivalent form does not change its value. What norm are you talking about? Norm[5*Sin[w*t - 2]] TrigToExp[5*Sin[w*t-2]] //Norm find the same thing, the absolute value of 5*Sin[w*t - 2], which changes with t, whether it's in terms of complex exponential functions or not. – Michael E2 Oct 18 '16 at 12:08
1

@DoHe Maybe you're thinking of this sort of approach?: http://i.stack.imgur.com/fSn0g.png – Michael E2 Oct 18 '16 at 12:09

1 Answers1