Curve Fitter CURVE FITTER Open Update Fit Save New Exclusion Rules Select Validation Data Polynomial Exponential Logarithmic Auto Fourier Fit Fit Duplicate Data Manual FILE DATA FIT TYPE FIT Harmonic Motion X us 0.45 mi ce 0.4 0.35 0.3 0.25 0.2 Residuals Plot Contour Plot Plot Prediction Bounds None VISUALIZATION Colormap Export PREFERENCES EXPORT Fit Options COA Fourier Equation Fit Plot x vs. t -Harmonic Motion a0+ a1*cos(x*w) + b1*sin(x*w) Number of terms Center and scale 1 ▸ Advanced Options Read about fit options Results Value Lower Upper 0.15 a0 0.1586 0.1551 0.1620 a1 0.0163 0.0115 0.0211 0.1 b1 0.0011 -0.0093 0.0115 W 1.0473 0.9880 1.1066 2 8 10 t 12 14 16 18 20 Goodness of Fit Value Table of Fits SSE 0.2671 Fit State Fit name Data Harmonic Motion x vs. t Fit type fourier1 R-square 0.13345 SSE DFE 0.26712 296 Adj R-sq 0.12467 RMSE 0.030041 # Coeff Valic R-square 0.1335 4 DFE 296.0000 Adj R-sq 0.1247 RMSE 0.0300

What point on the spring or different masses should be the place to measure the displacement of the spring? For instance, should you measure to the bottom of the hanging masses?

Let's assume that the brightness of a field-emission electron gun is given by β = 4iB π² d²α² a) Assuming a gun brightness of 5x108 A/(cm²sr), if we want to have an electron beam with a semi-convergence angle of 5 milliradian and a probe current of 1 nA, What will be the effective source size? (5 points) b) For the same electron gun, plot the dependence of the probe current on the parameter (dpa) for α = 2, 5, and 10 milliradian, respectively. Hint: use nm as the unit for the electron probe size and display the three plots on the same graph. (10 points)