Question

A piezoelectric accelerometer has a damping ratio of 0.65, a proof mass of 0.5 grams, and a spring rate of 10,000 N/mm. What is the damped natural frequency in hz of this device? (Type in an integer)

Hint: Make sure your units of measure are consistent first, then use the formulae to calculate the natural and damped natural frequencies.

Answer 1

The natural frequency in Hz of this device is

$$\omega_n=\sqrt{\frac{k}{m}}=\\\space\\=\sqrt{\frac{10000\text{ N/mm}\cdot1000\text{ mm/m}}{0.5\text{ g}\cdot10^{-3}\text{ kg/g}}}=141.4\cdot10^3\text{ Hz}.$$