Step Response for $q_0(t)$The step response of a measurement system, whose output is $q_o(t)$ and input is $q_i(t),$

is provided in Figure $4.$

$($a$)$ Determine the transfer function $G_4(s)$ relating $q_o(t)$ to $q_i(t)$ given that $q_i(t)$ is a unit step input.

$($b$)$ Obtain a differential equation that represents the measurement system.