Calculate the lowest frequency:

Indicate the lowest frequency for the seismometer along 1% error. The natural frequency is equal to 4 Hz and damping factor is equal to 0.2.

Solution

It is given that

Error = 1%

f_n = 4 Hz  & ζ = 0.2

1.0201 = {r ⁴ - 1.84 r ² + 1} = r ⁴

0.0201r ⁴  - 1.877 r ²  + 1.0201 = 0

r ⁴  - 93.38 + 50.75 = 0

It gives the following

 r = 9.63, 0.739

 For seismometer

r ≥ 1

∴ The lowest frequency that can be measured along 1% error is

9.63 × 4 = 38.54 Hz .