Transcription of Mass-Spring-Damper Systems The Theory
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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.
the displacement y will vary (unless it is a constant) as time, t, varies. However, in any given system M, λ and l will always take just the one value for all time. ... The Forced Mass-Spring-Damper System Consider now the case of the mass being subjected to a force, f(t), in the
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