Question

An elastic force sensor has an effeictive seismic mass of $0.1kg$, a spring stiffeness of $10N/m$ and a damping constant of $14N-s/m.$ Transfer function of the given force sensor relating displacment and force is given by

• A. $\frac{0.1}{{10}^{-2}{s}^2+1.4s+1}$
• B. $\frac{1}{{10}^{-2}{s}^2+1.4s+1}$
• C. $\frac{10}{s^2+140s+100}$
• D. $\frac{1}{s^2+140s+100}$

Answer 1

The correct option is C $\frac{10}{s^2+140s+100}$

$M=0.1kg,K=10N/m,D=14N-s/m$

Mathematical model of elastic sensor element.

$F\left(t\right)=M\frac{d^2{x}_0\left(t\right)}{d{t}^2}+D\frac{d{x}_0\left(t\right)}{dt}+K{x}_0\left(t\right)$

Apply Laplace tansform on both side,

$F\left(s\right)=(M{s}^2+Ds+K)x\left(s\right)$

Transfer function

$\frac{X_0\left(s\right)}{F\left(s\right)}=\frac{1}{M{s}^2+Ds+K}=\frac{1}{0.1s^2+14s+10}$

$\frac{X_0\left(s\right)}{F\left(s\right)}=\frac{10}{s^2+140s+100}$