Question

An accelerometer has a seismic mass of $0.05kg$ and a spring constant of $2\times {10}^{3}N/m$. If the maximum mass displacement is $+0.05m$ before the mass hits the stop. Then the maximum measurable acceleration is _____ $m/s^2.$

• A. 2000

Answer 1

The correct option is A 2000
$\text{Natural frequency}$

${\omega }_n=\sqrt{\frac{k}{m}}=\sqrt{\frac{2\times {10}^3}{0.05}}=200rad/sec$

$\text{Maximum acceleration}\left(a_m\right)={\omega }_n^2{x}_m$

$=(200{)}^2\times 0.05$

$=2000m/s^2$