I need help solving RC circuit using Leplace inverse, then graph the output which is in the symsum form

So I solved the following Ciruit using Leplace Transform, as I want to find the output on V3.

and this is what I got

then I used Symbolic Math Toolbox Laplace transforms .. with the following code

Ys2(s)=((2*s^2+7*s+3)/(2*s^3+11*s^2+15*s+4)*(2*s+2)/(2*s^2+7*s+3)*1/(s+1)*1/s)

yt = ilaplace(Ys2,s,t)

and this is the output

1/2 - symsum((exp(t*root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k))*root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k)^2)/(6*root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k)^2 + 22*root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k) + 15), k, 1, 3) - (15*symsum(exp(t*root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k))/(6*root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k)^2 + 22*root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k) + 15), k, 1, 3))/2 - (11*symsum((exp(root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k)*t)*root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k))/(22*root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k) + 6*root(z^3 + (11*z^2)/2 + (15*z)/2 + 2, z, k)^2 + 15), k, 1, 3))/2

Now I don't understand why I got my code in such a weirdo format? what did I do wrong?

And if nothing is wrong with this code, how to graph it?

I tried using syms, and declaring W and putting it equal to the output, but failed.

Any help is appreciated

Answer 1

[Star Strider]

Sometimes a bit fo force (such as using vpa) is necessary —

syms s t 
Ys2(s)=((2*s^2+7*s+3)/(2*s^3+11*s^2+15*s+4)*(2*s+2)/(2*s^2+7*s+3)*1/(s+1)*1/s)

Ys2(s) = 

yt = ilaplace(Ys2,s,t)

yt = 

yt = vpa(simplify(yt, 500),5)

yt = 

ytfcn = matlabFunction(yt)

ytfcn = function_handle with value:
    @(t)exp(t.*-3.514647277636355e-1).*-7.105148673541635e-1+exp(t.*-1.606599092554053).*2.562392432382694e-1-exp(t.*-3.541936179682311).*4.572437588399225e-2+5.0e-1

figure
fplot(ytfcn, [0, 50])
grid on

The matlabFunciton call is not absolutely necessary, however it may make life easier if the intent is to use ‘yt’ outside the Symbolic Math Toolbox.

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[Abdelrhman Abdelfatah]

oh woww, thank you so much for taking the time to help!

[Star Strider]

As always, my pleasure!

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