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%
fn = 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 .