# CU-Boulder MCEN 3037 - 25 (14 pages)

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- Pages:
- 14
- School:
- University of Colorado at Boulder
- Course:
- Mcen 3037 - Data Analysis

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yp kA sin t 1 2 n 2 2 2 n 2 2 n Arc tan 2 1 2 n Desired system behavior sometimes magnitude ratio 1 phase shift 0 Note from the forcing function n property of the system Magnitude ratio 1 around the resonance frequency for under damped cases Resonance frequency of under damped system occurs at D n 1 2 2 p phase shift occurs at resonance for undamped system characteristic of resonance Systems with a damping ratio of greater than 707 do not resonate Transmission band 3dB M 3dB Filter band M 3dB eliminate high frequency signals A strain gage measurement system is mounted on an airplane wing to measure wing oscillation and strain during wind gusts The strain system has a 90 rise time of 100 ms a ringing frequency of 1200 Hz and a damping ratio of 0 8 Estimate the dynamic error in the measurement of a 1Hz oscillation Also estimate any time lag Dynamic error M 1 What kind of system is this 2 1 n We are given the ringing frequency d Natural frequency n Drive frequency 2p d 1 2 2 p 1200 0 36 4000p We can plug in and find out M 1 2 n 2 2p 5 x10 4 n 4000p M 1 2 2 n 1 1 5x10 2 0 80 5x10 2 4 2 4 2 1 2 There is virtually no dynamic error in this system 2p How do we find the time delay td 2 4 2 0 8 5 x 10 Arc tan n Arc tan 2 4 2 1 5 x10 1 2 n 8x10 4 rad td 0 127ms Select one set of appropriate values for damping ratio and natural frequency for a second order instrument used to measure frequencies up to 100 rad s with no more than 10 dynamic error A catalog offers models with damping ratios of 0 4 1 and 2 and natural frequencies of 200 and 500 rad sec In the end we have to check these M 1 1 2 n 2 2 2 n 2 n n M M 1 200 4 5 1 18 0 18 200 1 0 5 64 0 36 200 2 0 5 47 0 53 500 4 2 1 03 0 03 500 1 0 2 96 0 04 500 2 0 2 80 0 20 1 The system is under damped 2 We have a static sensitivity of 1 0 mm mm and an input magnitude of 1 0 Therefore that magnitude ratio is M 5 The dynamic error is M 1 5 0 1 0 4 0 3 The time lag is 10 ms the phase lag is thus 2p 10 p rad 90deg rees 40 2 4 Assume we

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