Question

3) The figure below shows a model including two masses and three springs. The input is an external force f(t). Important: assume that mass2 will always remain horizontal - it cannot rotate! a) Clearly state all assumptions to be used for modeling this system. b) Draw the freebody diagrams. State your "presumptions" on the configuration of the states of the system. Be sure to label the magnitude and direction of the forces consistent with those presumptions. c) Use the freebody diagrams to derive the equations of motion (ODES) for the system. 1 ka x2 D ft)

Answer 1

Answer ! 9 i Applied external fora is such that deformation in the spring bears a linear relation ( for constant Stipprubs), (ii, Masses are assumed to be point masses, W springs are massless, all porses are acting on mans only. pre-assumptions! (i) Let H > a, (ii) Inestia force will act opposite to the motion FBD of "ma K2 (012 - and will be egnal to mass times accelesanish 1 1 ki M2 m2 % & Inertia goste. it me 1 Velt FBD glam," K3 © Tk2 (21-22) from past 'b' using FBI According to D'Alembertls principle, Inentia force - + Extermen ces = 0 Equation of motion posma min + K2 (211-012) + k34, 20. Egnation of motion for anal mär + KM₂ + kz (22-2) = f(t)