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an instrument having a resonance frequency of 1414 rad/s with a damping ratio of 0.5 is used to measure a signal of ~6000 hz. estimate the expected dynamic error and phase shift.

User Shians
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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))

User Kiril Aleksandrov
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