Stretch receptors in lungs are modeled as second-order systems whose input is the applied stretch, x(t), and output is the instantaneous firing frequency of the receptor, y(t). Assume that one such receptor can be described by the differential equation:
d^2y/dt^2 + 2*d/dt + 4y(t) = 10x(t) +dx/dt
Determine the frequency response of this receptor to stretching.
There are devices that can apply sinusoidal stretch to a small segment of tissue. Calculate the steady-state response, y(t), to stretching an airway segment according to x(t) = 2cos(pi*t)u(t).