how to plot Ilaplace results

Hello, I am trying to plot a inverse laplace equation, so far I have:

syms s;
M1 = -3.5;
D1 = 1;
M2 = 4;
D2 = 0.75;
T = 6.283;

inc_w1 = (-((M2*s+D2)*s+T))/((M1*s+D1)*((M2*s+D2)*s+T)+(M2*s+D2)*T);
inc_w1 = simplify(inc_w1);
ilap = ilaplace(inc_w1);

the output for ilap is:

"ilap = - 25132*sum(exp(r20*t)/(2*(- 84000*r20^2 + 5500*r20 + 7783)), r20 in RootOf(s20^3 - (11*s20^2)/112 - (7783*s20)/28000 - 6283/8000, s20)) - 3000*sum((r20*exp(r20*t))/(2*(- 84000*r20^2 + 5500*r20 + 7783)), r20 in RootOf(s20^3 - (11*s20^2)/112 - (7783*s20)/28000 - 6283/8000, s20)) - 16000*sum((r20^2*exp(r20*t))/(2*(- 84000*r20^2 + 5500*r20 + 7783)), r20 in RootOf(s20^3 - (11*s20^2)/112 - (7783*s20)/28000 - 6283/8000, s20))"

I followed the help step by step and this output has nothing to do with the F(t) I expect.

I understand more or less what matlab is trying say with this, but again what I need is an F(t) not a symbolic equation function of the roots of some polynomials.

So, what does this output means, and how can I plot the inverse lapace transform of my initial function inc_w1 for a vector of time, lets say t = 0:.1:10

     To sum up, how do I calculate a numeric Ilaplace(f(s))?

Any help is appreciated, thanks in advance.

Answer 1

[Christopher Creutzig]

I don't know what exactly you mean by “a numeric Ilaplace(f(s)),” but you can numerically approximate the constants in the transform with the vpa command:

>> vpa(ilap)

ans =

exp(t*(- 0.4807809811118731569778183223397 + 0.71409095427139567776813754964539*i))*(- 0.00046283581958834613528863495956936 + 0.15585312307864670868071337051094*i) + exp(t*(- 0.4807809811118731569778183223397 - 0.71409095427139567776813754964539*i))*(- 0.00046283581958834613528863495956936 - 0.15585312307864670868071337051094*i) + 0.28663995735346240655629155563342*exp(1.0597762479380320282413509303937*t)

Use digits to reduce the precision if this is too verbose.