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diffrent plots if I add the command assume (0<=t) why ?

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so I want to get laplace transform of f(t)=cos(12t)*exp(-0.4t). the strange this is that if add the command : assume (0<=t) I get the right laplace transform but the plot of f(t) is not starting from zero ,but insted start from -20 . hot to fix this problem ?
clc;clear all;
syms t
assume(0<=t);
f_t3 = piecewise(0<=t,cos(12*t)*exp(-0.4*t));
f_s3=laplace(f_t3);
pretty(f_s3)
fplot(f_t3,[-20 20]);
but if I write the same code but with out assume(0<=t) I get the right plot but not the right laplce transform of f(t) .
clc;clear all;
syms t
f_t3 = piecewise(t<0,0,0<=t,cos(12*t)*exp(-0.4*t));
f_s3=laplace(f_t3);
pretty(f_s3)
fplot(f_t3,[-20 20]);

Answers (2)

Walter Roberson
Walter Roberson on 23 Jul 2022
assume(0<=t);
You solemnly swear that t will never be complex or negative
fplot(f_t3,[-20 20]);
but you make t negative down to -20 anyhow.
  2 Comments
Paul
Paul on 23 Jul 2022
Let me see if I understand this correctly
syms t
assume(0<=t);
f_t3 = piecewise(0<=t,cos(12*t)*exp(-0.4*t))
f_t3 = 
So the piecewise is simplified away due to the assumption. laplace() works fine on f_t3. But then fplot() comes along and basically does a subs type of thing over [ -20 20 ] w/o caring about the assumption.
In the second case, fplot has no reason not to work, but laplace() and piecewise() just don't play nice together. I'm not quite sure why that has to be the case, but I'm really not suprised.
Is that about right?

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Paul
Paul on 23 Jul 2022
I suggest getting in the habit of using heaviside for problems like this
syms t
f_t3 = cos(12*t)*exp(-0.4*t)*heaviside(t);
f_s3=laplace(f_t3)
f_s3 = 
fplot(f_t3,[-20 20]);

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