Final answer:
The expected dynamic error can be calculated by finding the difference between the resonance frequency and the signal frequency. The phase shift can be determined using the damping ratio.
Step-by-step explanation:
Resonance frequency of an instrument with a damping ratio of 0.5 is 1414 rad/s.
The signal frequency to be measured is ~6000 Hz.
To estimate the expected dynamic error, we need to calculate the difference between the resonance frequency and the signal frequency:
Dynamic Error = |Resonance Frequency - Signal Frequency|
Dynamic Error = |1414 rad/s - 6000 Hz|
Phase shift in a damped system can be determined using the damping ratio. The phase shift is given by the formula:
Phase Shift = arctan(damping ratio / sqrt(1 - damping ratio^2))
Phase Shift = arctan(0.5 / sqrt(1 - 0.5^2))