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

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]);

Answer 1

[Walter Roberson]

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.

[Paul]

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?

[tomer polsky]

thank you

Answer 2

[Paul]

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]);

[tomer polsky]

thank you very much !