Dynamic_systems_lab

# Dynamic_systems_lab - Name Date of lab Section number M E...

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Name: ______________________________________________ Date of lab: ______________________ Section number: M E 345._______ Lab 9 Precalculations – Individual Portion Dynamic Systems Lab: Dynamic Systems Response Precalculations Score (for instructor or TA use only): _____ / 20 1. Calculate the time constant for a first-order low-pass RC filter circuit. Give your answer in equation form, namely τ as a function of resistance R and capacitance C . 2. For a low-pass filter with R = 100 kohm and C = 1.0 microfarad, calculate the time constant in seconds. Show all unit conversions. 3. Suppose the peak displacement amplitude is measured over some finite time for an oscillating spring-mass- damper system. The first peak amplitude y 1 is 1.58 cm. The twentieth peak amplitude y 20 is 0.61 cm. Calculate the log decrement and the damping ratio for this case, showing all your work.

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Cover Page for Lab 9 Lab Report – Group Portion Dynamic Systems Lab: Dynamic Systems Response Name 1: ___________________________________________________ Section M E 345._______ Name 2: ___________________________________________________ Section M E 345._______ Name 3: ___________________________________________________ Section M E 345._______ [Name 4: ___________________________________________________ Section M E 345._______ ] Date when the lab was performed: ______________________ Group Lab Report Score (For instructor or TA use only) : Lab experiment and results, plots, tables, etc. _____ / 50 Discussion _____ / 20 Neatness & grammar _____ / 10 TOTAL ______ / 80 Comments (For instructor or TA use only) : NOTE: The instructor or TA reserves the right to deduct points for any of the following: Arriving late to lab or leaving before your lab group is finished. Not participating in the work of your lab group (freeloading). Causing distractions, arguing, or not paying attention during lab. Other (at the discretion of the instructor or TA).
Dynamic Systems Lab: Dynamic Systems Response Author: John M. Cimbala, Penn State University Latest revision: 13 November 2007 Introduction and Background ( Note : To save paper, you do not need to print this section for your lab report.) Some students are having trouble understanding input impedance . Therefore a small part of this lab will help clear up some misconceptions about this. First-order and second-order dynamic systems were discussed in detail in the lectures, and a few physical examples of each were given. In this lab, electrical circuits will be used to illustrate first- order and second-order dynamic system response, and an oscillating spring-mass system will be used to illustrate second-order dynamic system response. V i R 1 V o I Input Impedance : Consider current I passing through resistor R 1 from voltage V i to V o as sketched to the right. If the voltmeter or DMM measuring voltage V o has an infinite input impedance, V o exactly equals V i , and the current I passing through the resistor is zero. Any real voltage measurement device, however, has a non-infinite input impedance. The actual circuit behaves more like the circuit to the right, where the input impedance of the DMM is shown as resistor R 2 . This circuit now acts as a voltage divider, with 2 o 12 i R VV R R = + . The current is no longer zero, and V o is smaller than V i . In this lab, you will measure the output voltage for several values of R 1 , and then calculate the input impedance of the DMM.

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Dynamic_systems_lab - Name Date of lab Section number M E...

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