1. Mechanical Translational systems Group A: Keith Brisbane Charlie Kreiner Jacek Sienkiel Adam Sparks Himanshu Suri Mae340 Lab 1

2. Background In this experiment we used a strain gage and a potentiometer to explore the characteristics of a mechanical spring as a system component and the natural second order behavior of a mass-spring system.

3. Materials The potentiometer is a variable resistor that changes voltage based on displacement. The strain gage measures the difference in voltage that results from the stess (force) applied to the strain gage. The analog to digital converter translates the analog voltage output signals into data the computer can interpret so we can record the data necessary to do our calculations. The spring.

4. Methods First we used a ruler and measured the voltage at different positions that were +/-.5 inches from equilibrium. Then we used this data to calibrate the potentiometer. Second we placed weights on the strain gage (vertically, using gravity to find the force on the gage) and measured the voltages. We used this data to calibrate the strain gage. Finally we used the calibration data from the previous steps to calculate the spring stiffness(k) and the transient response of the spring mass system.

5. Results

6. Potentiometer calibration x(m)V(V) 03.28 0.006353.52 0.01273.72 0.019053.9 0.02544.04

7. Strain Gage Calibration mass(g)Force(N)voltage(mV) 0027.8 3002.94319.33 6005.88610.65 854.38.3806833.55

8. Spring Constant Calculation

9. Transient Response ωd=2π/T= 2π/.128=49.087rad/s; ƒd=1/.128=7.813hz.128 is the period as estimated from the graph. δ=1/N*ln[xk/xk+N]=1/1*ln[.0156/.0053]=1.0581 xk and xk+N are the displacements at the 1st and 2nd peaks. ζ=δ/√[(2π^2)+δ^2]=1.0581/√[(2π^2)+1.0581^2]=.1661 ωn= ωd /√(1-ζ^2)= 49.087 /√(1-.1661^2)=49.779rad/s x(t) =Ce^(-ζωnt)cos(ωdt) => x(t) =-0.023e^(-8.266t)cos(49.09t)

10. Discussion The transient response mimics the second order system, which supports our motivation for doing the lab. When working in the lab the affects of resistance in wires, friction, resolution of the ADC, and air resistance are all assumed to be negligible. The role of the simulation serves as a way to compare our data to an ideal transient response.