The article gives an account of an experiment in which sixty-eight high school students of age 16 -19 developed spreadsheet applications that simulated fall and projectile motion in the air. The students applied the Euler method to solve the governing differential equations. The aim was to promote STEM to the students and motivate them to study STEM at universities. A questionnaire survey was carried out to find out if the participants found the lessons interesting and if developing and using the spreadsheet models benefited the learning and contributed to the mathematical and technological knowledge of the students.
A time explicit fast converging exact power series solution to the pendulum equation is derived in this paper. A novel series for the period results from it. The approximate formula that comprises the first three terms gives an accuracy of 99.99% up to the amplitude of 90°. The accuracy was compared with that of 11 other approximate period formulas.
This paper gives the solution and analysis of projectile motion in a vacuum if the launch and impact heights are not equal. Formulas for the maximum horizontal range and the corresponding angle are derived. An Excel application that simulates the motion is also presented, and the result of an experiment in which 38 secondary school students developed the application and investigated the system is given. A questionnaire survey was carried out to find out whether the students found the lessons interesting, learned new skills and wanted to model projectile motion in the air as an example of more realistic motion. The results are discussed.
This article deals with simultaneous measurements of three mutually orthogonal thermal diffusivities of a material with orthogonal anisotropy using the flash method. Unlike the conventional flash method, the modified measuring technique considers pulse heating over a rectangular area of the front face of a wall-shaped sample of an orthotropic composite material. The thermal diffusivities are calculated analyzing the temperature rise versus time evolutions when measured simultaneously at various positions on the sample surface. This article presents a data reduction method that enables estimates of the thermal diffusivities for the three principal axes. The theory takes into account heat losses from the front and rear faces. The results of an experimental design analysis are discussed.
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