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Mass-Spring-Damper Systems The Theory

Mass-Spring-Damper Systems : The , Bournemouth University 2001 Page 1 of 9 Mass-Spring-Damper SystemsThe TheoryThe Unforced Mass- spring SystemThe diagram shows a mass, M, suspended from a spring of naturallength l and modulus of elasticity . If the elastic limit of the springis not exceeded and the mass hangs in equilibrium, the spring willextend by an amount, e, such that by Hooke s Law the tension in thespring, T, will be given by Tel= For system equilibrium, this will be balanced by the weightso leTMg == (1)If the spring is pulled down a further distance, y, (with y positive downwards) therestoring force will now be the new tension in the spring , T, given by () =+Teyl ,and so the net force acting DOWNWARDS is MgT ()= += MgeylMgelyl.

Here, R is the constant of proportionality and is called the damping factor. ... dependent upon the viscosity of the fluid in the dashpot, for example. The Forced Mass-Spring-Damper System Consider now the case of the mass being subjected to a force, f(t), in the direction of motion.

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