Question

You need to select a device to measure a signal at 250 Hz with no more than a 2% loss of amplitude.   A line of instruments is available that has a fixed natural frequency of 600 Hz, but the line has a range of damping coefficients. Which of the following damping coefficients would be appropriate?

a) 0.54

b) 0.60

c) 0.66

d) 0.75

e) 0.48

Answer 1

The  time displacement relationship for a forced vibration equation

is given by

Where 'f' is the amplitude per unit mass of applied external force.

'p' is driving frequency = 250Hz

'b' is damping cofficient

is natural frequency = 600Hz

The amplitude of the oscillation is given by

Amplitude is maximum ( Amplitude resonance) when and maximum amplitude we get is

By the problem statement

Or

Or

Or squaring both sides we get

Or

Or

Or

Or

b=2915.5