Question

An accelerometer can be modeled as a second order dv dv 2 dt Problem 3: system: dt the acceleration. m, c, and k are the physical properties o where v is the output voltage and a is m the accelerometer: mass, damping coefficient and stiffiness y. natural fiequency, damping ratio and sensitvity er (a) What of the 2018 A sinusoid has been sampled poorly. The result is shown belo could independently explain this misrepresentation e. w. List two errors that 0.3 0.7 1.2 1.6 Time (sec)

Answer 1

$m\frac{d^2 v}{dt^2}+c\frac{dv}{dt}+k v = Ba$

Laplace transform:

$\frac {V(s)} {A(s)}= \frac{B} {(ms^2+cs+k)}$

$\frac {V(s)} {A(s)}= \frac{B} {m}*\frac{1}{(s^2+(c/m)s+(k/m))}$

roots of the quadratic equation in the denominator are:

$\frac{-(c/m)\pm \sqrt ((c/m)^2 - 4(k/m))}{2}$

$-(c/2m)\pm \sqrt(c^2/4m^2 - (k/m)$

$w_n = \sqrt(k/m)$ - Natural frequency

$2\zeta w_n = c/m\Rightarrow \zeta = \frac{c}{2\sqrt(km)}$ - Damping ratio

b and c )

07wn J 26