1.The dynamics of a first-order sensor can be described by
where x(t) is input, y(t) is output and τ is a constant. Consider a pulse input withamplitude k and duration T as shown below, i.e., x(t) = k, 0 ≤ t ≤ T and x(t) = 0,
t ≥T. Find and plot the output of the sensor corresponding to this input.

2. In last question suppose that amplitude of the pulse k = ˆk/T where ˆk is a
constant and T is the duration of the pulse. In this case pulse amplitude is inversely
proportional to its duration. Find the output y(t) when T →0. Plot y(t) in this limit
and comment on your plot.

dt 0 = (0)f = (0)x (7)2 = (})6 + (ap-