E11 Lab #5
Post-lab
2008

Second Order Time Domain Response

This lab requires a formal lab report.

If you are having a lot of trouble with part of the report, please come see me.  I don't want the writing of the lab report to be an exercise in frustration, so if you get stuck, please don't hesitate to ask for help.  Also, if you find you are missing some data, or it just doesn't make sense, please talk to me before finishing your report.

### Be sure to include in your report: (you should think quite hard about the organization of the report)

• Derivations of differential equations for the two circuits (RLC and op-amp).
• Solutions of the differential equations; one for ζ<1 and one for ζ>1.
• All pertinent oscilloscope data.
• All the Multisim simulations that you performed (in a way that can be easily compared to corresponding oscilloscope outputs and expected results).
• Either:
• Calculations and plots of the expected response (using the expected values of ω0 and ζ). Compare the expected response to the screen shots (e.g., show them side by side). Compare expected and experimental values of α and ωd for the cases where R=100 and R=1000 Ω.
...or...
• A best fit of the data collected from the oscilloscope.  From the fit determine ω0 and ζ, and compare to the expected values (note: you can use the expected values as the initial guess for the fit).  You should also compare the best fit parameters with values of α and ωd taken directly from the step response (by measuring period and decay of oscillations) for the cases where R=100 and R=1000 Ω, and for the op-amp circuit.  You will get one point of extra credit for each successful curve fit.
• In either case, note that the form of the equations representing the output are different for ζ<1 and ζ>1.
• Direct comparison of theory and experiment whenever possible.
• Describe the qualitative effects of varying C and R in first circuit (and give a brief explanation).

It may be helpful to recall that the Wavetek function generator can be modeled as shown (where Vs is an ideal source):