A MEMS-based accelerometer has a mass of m = 2 grams, an equivalent spring constant of k = 5 N/m, and an equivalent damping coefficient of c = 0.1 N∙s/m. Determine the natural frequency  n and the damping ratio .

The natural frequency = 50 rad/s = 7.96 Hz

Damping ratio = 0.5

Explanation:

The natural frequency is calculated in this manner

w = √ (k/m)

k = spring constant = 5 N/m

m = mass = 2 g = 0.002 kg

w = √ (5/0.002) = 50 rad/s

w = 2πf

50 = 2πf

f = 50 / (2π) = 7.96 Hz

Damping ratio = c/[2√ (mk) ] = 0.1 / (2 * √ (5 * 0.002)) = 0.5