Figure P3.43 shows two systems (a) and (b), which may be used to study force transmissibility and motion transmissibility, respectively. Clearly discuss whether the force transmissibility Fs /F (in the Laplace domain) in system (a) is equal to the motion transmissibility Vm/V (in the Laplace domain) in system (b), by carrying out the following steps:
1. Draw the linear graphs for the two systems and mark the mobility functions for all the branches (except the source elements).
2. Simplify the two linear graphs by combining branches as appropriate (series branches: add mobilities; parallel branches; inverse rule applies for mobilities) and mark the mobilities of the combined branches.
3. Based on the objectives of the problem, i.e., determination of the force transmissibility of system (a), and motion transmissibility of system (b), for applying Thevenin's theorem, determine which part of the circuit (linear graph) should be cut (Note: The variable of interest in the particular transmissibility function should be associated with the part of the circuit that is cut).
4. Based on the objectives of the problem, establish whether Thevenin equivalence or Norton equivalence is needed (specifically: use Thevenin equivalence if a through variable needs to be determined, because this gives two series elements with a common through variable. Use Norton equivalence if an across variable needs to be determined, because this gives two parallel elements with a common across variable).
5. Determine the equivalent sources and mobilities of the equivalent circuits of the two systems.
6. Using the two equivalent circuits determine the transmissibility functions of interest.
7. By analysis, examine whether the two mobility functions obtained in this manner are equivalent.
Figure P3.43
