Experiment for spline interpolation and integration


Background:

The motivation behind the experiment is to understand spline interpolation and numerical integration by finding the volume of water that can be held by a champagne glass.

What does the student do in the lab:

The student chooses one of the odd-shaped champagne glasses (Figure 1). The student measures the outer radius of the champagne glass at different known locations along the height. The student measures the thickness of the glass, so that he/she will be able to find the inner radius of the champagne glass at the locations he/she measured the outer radius. The student pours water to the brim in the champagne glass and checks how much volume the champagne glass holds.

Champagne GlassExercises assigned to the students:
Use MATLAB to solve problems. Use comments, display commands and fprintf statements, sensible variable names and units to explain your work. Staple all the work in the following sequence. Use USCS system of units throughout.

  1. Attach the data sheet on which you collected the data in class.
  2. Find the spline interpolant that curve fits the radius vs height data.
  3. Show the individual points and the spline interpolant of radius vs height on a single plot.
  4. Find how much volume of water the champagne glass would hold.
  5. Compare the above result from problem#4 to the actual volume.
  6. In 100-200 words, type out your conclusions using a word processor. Any formulas should be shown using an equation editor. Any sketches need to be drawn using a drawing software such as Word Drawing. Any plots can be imported from MATLAB.

What materials do you need; where do I buy it; how much do the materials costs?

  1. Champagne Glasses: These glasses, called the Hurricane Plastic Glasses, are available at www.poolsidepineapple.com, part nos. HUR-105, HUR-106, YAR-114. We used glasses made of plastic to avoid breakage. http:/www.poolsidepineapple.com/cart_pages/shopping%20page%20tropical.htm. You can try other places to buy the champagne glasses. About $40 or so for about six pieces including S&H. Better yet, go to a cruise and get souvenir glasses. Whenever you do the experiment, you will remember the good times.
  2. Graduated Cylinder: The graduated cylinder is available at http://scientificsonline.com/, part number 3036286. The cost of the cylinder is $20+S&H.
  3. Vernier Caliper: The caliper is available at http://mcmaster.com part number 20265A49. The cost of the vernier caliper is $60+S&H.
  4. Scale: Need to buy a thin scale for this. Any art-supplies store for $2 or so.

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This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu

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Autar Kaw

Autar Kaw (http://autarkaw.com) is a Professor of Mechanical Engineering at the University of South Florida. He has been at USF since 1987, the same year in which he received his Ph. D. in Engineering Mechanics from Clemson University. He is a recipient of the 2012 U.S. Professor of the Year Award. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. The OpenCourseWare (nm.MathForCollege.com) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. Petersburg Times and Tampa Tribune.

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