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Waveform analysis and inverse Laplace transforms

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1. For the waveform shown in FIGURE 1 (see attached file), estimate:
(a) the damping factor (you may compare response with a standard chart)
(b) the forced or damped frequency of oscillation
(c) the natural or undamped frequency

2. Complete the following inverse Laplace transforms (see attached files)

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Solution Summary

This solution provides an analysis of a given underdamped waveform to determine the natural frequency, damped frequency and damping factor using peak values from the waveform and logarithmic decrement analysis tools. The second part shows solutions of some inverse laplace transform examples including some using partial fraction expansion to deriuve the standard inverse Laplace transform representation

See Also This Related BrainMass Solution

Match each waveform with its causing transfer function.

The waveforms of FIGURE 2 were produced by the circuit of FIGURE 3. In FIGURE 3, LAP1 is a Laplace block transfer function.

Match each waveform A, B, C and D with its causing transfer function (1), (2), (3) and (4) given in TABLE A.

The filter responses to be matched with the waveform options are

a) 1/{s*2 + 2s + 2}

b) 1/{s^2 + s + 2}

c) 1/{s^2 + 0.5s + 2}

d) 1/{s^2 + 0.4s + 4}

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