Question

A measurement system with input x(t) and output y(t) is described by the differential equation $3\frac{dy}{dt}+5y=8x.$ The static sensitivity of the system is

• A. 0.60
• B. 1.60
• C. 1.67
• D. 2.67

Answer 1

The correct option is B 1.60

Differential equation,

$3\frac{dy}{dt}+5y=8x$

This is a first-order system.
First order standard equation

$\tau \frac{dy\left(t\right)}{dt}+y\left(t\right)=k.x\left(t\right)$

where k is the static sensitivity.

From equation (i),

$\frac{3}{5}\frac{dy}{dt}+y=\frac{8}{5}x$

$\therefore k=\frac{8}{5}=1.6$