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  3. 3 consider the mechanical system shown in fig 1 where...

Question: 3 consider the mechanical system shown in fig 1 where...

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3) Consider the mechanical system shown in Fig. 1, where a spring and a dampener (also known as a strut, or dashpot) are connected in parallel to a mass, mi. A force balance can be used to model the system in the same way a mass balance can be used to model a tank flow problem. F(t) is an external force applied to mi, F, is the force exerted by the spring, and Fa is the force exerted by the dashpot. Assume the spring obeys a linear relationship between force, Fs, and displacement, x, such that F, k,x, and that the force-displacement relationship of the dashpot is Fa fvdx/dt. a. Model the unsteady state response of this system using a force balance around mass mi. You should arrive at: dx dr dt 3 dt b. Solve this ODE via L.T.s, using the values: F(t) 5S(t) and x(0) 0, and x (0) 0 Figure 1. Spring and dashpot connected in parallel to a mass, mi.

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