MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
5th Edition
ISBN: 9781118629864
Author: Amos Gilat
Publisher: WILEY
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Chapter 11, Problem 9P

The relation between the tension T and the steady shortening velocity v in a muscle is given by the Hill equation:

(T+a)(v+b) = (T0+a)b

where a and b are positive constants and T0is the isometric tension. i.e., the tension in the muscle when v = 0. The maximum shortening velocity occurs when T = 0.

(a) Using symbolic operations, create the Hill equation as a symbolic expression. Then use subs to substitute T = 0, and finally solve for v to show that vmax=bT0)/a. (b) Use vmax from part (a) to eliminate the constant b from the Hill equation, and show that v=a(T0T)T(T+a)0vmax .

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