How does the step function work?

Hello, I am trying to figure out how the 'step' function work. I have a transfer function:

num = [-5.21];
den = [1 6 73];
G = tf(num, den);

Getting the inverse laplace of this transfer function manually, I get:

y(t)=((-5.21)/8)*exp(-3t)*sin(8t)

When I use the 'step' function the final steady state in the graph is -0.0714, when the final steady state of the inverse laplace approaches 0. There are great differences too in the graphs as the one worked manually it shows that the oscillation first peaks at -0.39 while matlab shows the first oscillation first peaks at -0.09. Where did I go wrong? I would greatly appreciate an answer. Thanks!

Matlab:

Desmos:

Answer 1

[Star Strider]

You forgot to actually use the Heaviside unit step function as an input!

num = [-5.21];
den = [1 6 73];
G = tf(num, den)

G =
 
      -5.21
  --------------
  s^2 + 6 s + 73
 
Continuous-time transfer function.

syms s t 
H = num /  poly2sym(den,s) * laplace(heaviside(t))

H = 

h = ilaplace(H)

h = 

figure
hfp = fplot(h, [0 2]);
grid

EndVal = hfp.YData(end)

EndVal = -0.0716

So the step result is correct!

.

[Arcadius]

That was right, thank you :)

[Star Strider]

As always, my pleasure!