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)