In this paper we develop the study of the oscillatory movement of a mass-spring system to illustrate the use of differential equations in the development of mathematical models for the simulation of physical situations and the interest on developing computational modules using a spreadsheet to be used as structured tools to support the modelling and the analysis of the results.

We first present the physics and mathematics foundations that lead to the differential equation that describes the oscillatory movement and its general solution. We study several particular solutions based on different initial conditions. Then we use a rightly structured spreadsheet to interpret the different solutions we obtained, using sensibility response studies to the several parameters supported by adequate graphic representations. Our goal is to show how the development of computational interactive modules, with good graphic capacities and animations, can improve the study, in an integrated way, of mathematical concepts in different areas, developing the capacity to establish connections between several mathematical fields.

We present some essential procedures to construct, using Excel, interactive applications to support the modelling problem we are dealing with.

mass_spring_system.xls (530 kB)
Excel file