Electrical – How to pass a square wave through transfer function in MATLAB

The step is a stimulus to the system. The system is defined by the pole zero diagram irrespective of the stimulus and it looks like a 2nd order response so here's the math behind the poles: -

You have poles at co-ordinates -5 on the real part of the s-plane and +/-9 on the \$j\omega\$ of the s-plane. So you can say 5 = \$\zeta\omega_n\$ and 9 = \$\omega_n\sqrt{1-\zeta^2}\$. From this you can work out what \$\omega_n\$ and \$\zeta\$ are.

Because it looks like a 2nd order system you can use this to define the shape from the above values for \$\omega_n\$ and \$\zeta\$: -

You must raise the equilibrium equations of the circuit (applying LKV, LKC and Ohm's Law), and then apply the Laplace Transform, considering that the initial conditions must be zero.
Next, you must operate to find an expression for \$V_o(s)\$ depending on \$V_i(s)\$.

Then, the trasfer function is:

$$ G(s) = \dfrac{V_o(s)}{V_i(s)} $$

Remember that

$$ L\quad\overset{\text{Laplace domain}}{\to}\quad s\cdot L\\ C\quad\overset{\text{Laplace domain}}{\to}\quad \dfrac{1}{s\cdot C} $$