MATLAB: Is simplification of ilaplace possible

Question

Hi you all! I must say YES, I'm student, and NO, this is not homework.

Function ilaplace doesn't work in computers of my university, and further I trully doubt my teacher know that it exists. But I like going beyond what I'm suppose to learn, and…

“Tell me and I forget, teach me and I may remember, involve me and I learn.”

― Benjamin Franklin

The function ilaplace gives a soltuion, which is not simplify, I'd thank a solution for this.

For an example code:

% declare tf
s=tf('s');
F_tf=5*(-1+1j)/(s+500j)+5*(-1-1j)/(s-500j);
F_tf=zpk(F_tf)%quick view of poles and zeros
F_tf=tf(F_tf);
num=F_tf.num{1};
den=F_tf.den{1};
% get inverse laplace of transfer function
syms s t % declare syms variables
F_sym=poly2sym(num,s)/poly2sym(den,s)
F_time=ilaplace(F_sym);
pretty(F_time) %another not simplified view

The resault is of class sym:

F_time =
(655360000*4294967296000001^(1/2)*sin((4294967296000001^(1/2)*t)/131072))/4294967296000001 - 10*cos((4294967296000001^(1/2)*t)/131072)

This is what must be simplified. Operating throught Command Window, and no Editor as i wanted, it solves to

f(t)=10*sin(500t)-10*cos(500t)

Answer 1

Here the expression is already simplified i.e., it is in the final form of sines and cosines. Since you want to change the fractions to decimal, variable precision arithmetic (vpa) should work!

F_time=ilaplace(F_sym);
F_time=vpa(F_time,2)
pretty(F_time)