Transcript LectureX
PH15010 Laboratory Techniques An Introduction to MATHCAD Simple X-Y plots • ‘Quickplot’ • Plot functions with 1 parameter • Use with built-in & user defined • Insert|Graph|X-Y plot Simple X-Y Plot #1 Y-axis placeholder X-axis placeholder Sizing grab-handle Simple X-Y Plot #2 Plot of sin(x) vs x 1 0.5 sin ( x) 0 0.5 1 10 5 0 x 5 10 Plot Formatting • Double click in graph • Format|Graph|X-Y Plot… • Dialog box – Gridlines, Numbered Axes, Log Scales – Traces: Colour, Points, Lines &c – Axis titles, legend – Defaults Doing More with Plots #1 • Add more curves to y-axis • Fix scale on x- & y-axis • Add markers on x- & y-axis - from dialog box Scaling plot axes y-axis scale placeholders 22.754 30 20 10 sin ( x) cos ( x) 0 tan ( x) 10 20 22.754 30 10 10 x-axis scale placeholders 5 0 x 5 10 10 Doing More with Plots #2 2 2 1 sin ( x) cos ( x) 0 tan ( x) 1 2 2 4 4 3 2 1 0 x 1 2 3 4 4 Dealing with Experimental Data • 5 stage process – – – – – Get data into MathCAD Process data (scale, units etc) Plot Data Fit curve (line) to data Compare theory with experiment Getting Data into MathCAD • Put data in matrix – 1 column per measurement – 1 row per data point • Use Input Table – Insert|Component|Input Table • Table re-sizes & scrolls as needed Data Input Example • Resistor Experiment • Apply voltage, measure Current Voltage Current (mA) Readings 0 0 1 2 3 4 5 6 1 0 1 2 3 4 0 1.23 2.45 3.7 4.92 1 row per reading pair Process Experimental Data #1 • Extract columns with column operator M<> – Insert into worksheet from • Matrix toolbar • <ctrl>-6 – Fill in column number to extract – Numbering starts at 0 Process Experimental Data #2 Readings 0 0 1 2 3 4 1 0 1 2 3 4 0 VApplied Readings V 1 IMeas ured Readings mA 0 1.23 2.45 3.7 4.92 Input table as before Extract Voltage to vector & apply units Same for current Check on extracted vectors • Single column • Converted to base units • Scroll bars if needed 0 1 VApplied 2 V 0 1.23 10 3 IMeas ured 2.45 10 3 3 3.7 10 4 4.92 10 3 3 A Plotting data • X-Y Plot can plot 1 vector against another, if both vectors have same number of elements • Use plot formatting to change to single points Plotting data Example 3 4.92 10 0.006 0.004 IMeasured 0.002 0 0 0 0 1 2 VApplied 3 4 4 Fit curve/line to data • Only simple straight line fits for now – slope(Vx,Vy) – intercept(Vx,Vy) • Details in help system • Units carry through calculation • Sometimes need 1/slope Slope calculation -Resistor Example RMeas ured 1 s lope( VApplied IMeas ured) RMeas ured 812.348 Compare theory to experiment • Create function • Plot on same graph as experimental data • Use multiple variables on x- and y- axes • Separate items on axes with commas Compare theory to experiment ITheory( vv) • Function gives theoretical current vv RMeas ured ITheory( 1 V) 1.231 mA ITheory( 2 V) 2.462 10 3 A • Test function at a couple of points Plot theory & data 3 6.15510 Multiple items on x& y-axes 0.006 IMeasured ITheory ( vv ) ‘vv’ exists only to make the plot 0.008 0.004 0.002 0 0 0 0 Scale x-axis to suit 1 2 3 VApplied vv 4 5 5