This problem was contributed by Carmichael Ong at Stanford University.

An experiment is performed in which a muscle–tendon unit is fixed at an unknown length, the muscle is activated to a predetermined level, and the tendon force is measured once the muscle and tendon have reached equilibrium (i.e., muscle and tendon forces are equal). The muscle has the following active and passive 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 (specified activation and measured tendon force), calculate the length of the muscle and the length of the tendon .

(a) ,

(b) ,

(c) ,

(d) ,

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