Transfer Function

The transfer function in this example can similarly be found using voltage divider rule:

$$H(s) = \frac{V_C(s)}{V_e(s)} = \frac{\left(Ls\left\Vert\frac{1}{Cs}\right.\right)}{R+\left(Ls\left\Vert\frac{1}{Cs}\right.\right)} = \frac{1}{RC}\cdot\frac{s}{s^2 + \frac{1}{RC} s + \frac{1}{LC}} \isdef 2\eta\cdot\frac{s}{s^2 + 2\eta s + \omega_0^2}$$