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This problem was contributed by Carmichael Ong at Stanford University.


An experiment is performed in which a muscle–tendon unit is fixed at some (unknown) length , the muscle is activated to a specified level, and the force is measured after the muscle and tendon reach equilibrium (steady state). The muscle has the following force–length relationships:

The tendon has the following force–strain relationship:

The muscle and tendon parameters are , , , and pennation .


For each of the following experimental conditions, calculate  and .

(a) , 

(b) , 

(c) , 

(d) , 


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