A pressure transducer that behaves as a second order system is used to monitor pressure fluctuations in a petrochemical pipeline. It is designed to have an undamped natural frequency of 4000 Hz. However, because it is damaged its damping ratio is unknown. When the transducer is subjected to a harmonic input of 2400 Hz, the phase angle between the output and input is measured at 45 degrees.
i.) Based on the above conditions, determine the error when the transducer is used to measure a harmonic pressure signal of 1600 Hz.
ii.) What is the phase angle between the input and output at this frequency?
iii.) Using excel obtain plots of the frequency response and phase response to harmonic excitation signal of 5000 Hz base conditions sited in the problem statement. Is the transducers' response characteristics suited to the application?