Translating Mechanical Systems Background

Animation by Ames Bielenberg


 This page describes translating mechanical systems (that is, systems that move back and forth in a straight line (i.e., translate)).  Because the systems only move along a single axis, we can generally neglect the fact that force is a vector (i.e., its direction will be collinear with the axis of motion).  Our discussion will also be limited in several other ways listed, and briefly discussed, here.

A list of the fundamental units of interest is listed below.  The next tab (system elements) gives a description of the building blocks of these system (mass, spring and friction elements). This is followed by a description of  methods to go from a drawing of a system to a mathematical model of a system in the form of differential equations.  Methods for solving the equation are given elsewhere.  The last section discusses topics relevant to energy storage and dissipation in these systems.

This page does not discuss the solution of these equations, only the development of the equations through a physical model of the system.

Table of units

The table below lists commonly used units of measure for translating mechanical systems in SI units.  More complete tables are available.


Fundamental Quantities   SI unit
Time - t second (s)
Mass - m kilogram (kg)
Length - l meter (m)
Force - f Newton (N)
Energy - w Joule (J) [W-s, N-m]
Power - p Watt (W) [J/s]
Spring Constant - k (N/m)
Friction Coefficient - b  (N-s/m)


© Copyright 2005 to 2019 Erik Cheever    This page may be freely used for educational purposes.

Erik Cheever       Department of Engineering         Swarthmore College