Casual Introduction to Numerical Methods – spring-mass-damper system model – part#5

In this tutorial, most of the calculations for the numerical simulation a SMD (spring-mas-damper) system will be consolidated into a single formula, the coordinate formula. In this case, in order to calculate the coordinate at the end of a any time step, we will need just the coordinates from the previous two time steps and of course the input parameters (constants). These input parameters are: mass, damping ratio, spring constant and time…

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Casual Introduction to Numerical Methods – a spring-mass-damper system model – part#3

Here is the third part of a tutorial in both elementary dynamics and numerical methods. It is written at a basic level and it shows you how to set up a dynamic model for numerical solving of simple differential equations.   The dynamic model makes use of an infinite loop, which make the calculations advance in time. Instead of a large table with formulas, this time we have a small number of…

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Modeling a Three-Pendulum Harmonograph – tutorial: part #2

Hi guys, here is the second part of a tutorial describing the matematical equations used in modeling a three-pendulum harmonograph (automatic drawing machine). It pertains to the second version of the model. This section describes the kinematic equations involved in the articulated linkage mechanism on the top of the table, the custom spreadsheet functions used in the model and some overall considerations about the partition of the spreadsheet.  This is an…

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Modeling a Three-Pendulum Harmonograph – tutorial: part #1

Hi guys, here is the first part of a tutorial describing the matematical equations used in modeling a three-pendulum harmonograph (automatic drawing machine). It pertains to the second version of the model. This section refers only to the kinematic equations for the movement of three pendulums. A second section will be published later and it will describe the kinematic equations involved in the articulated linkage mechanism on the top of the table,…

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