Instructions:

$1.$ Create the program using MATLAB

$2.$ Solve the following problem:

Problem

The mechanical power output $P$ in a contracting muscle is given by:

$P=T**v=kv{T}_o(\frac{1-\frac{v}{v_{\text{m}\text{a}\text{x}}}}{k+\frac{v}{v_{\text{m}\text{a}\text{x}}}})$

Where $T$ is the muscle tension, $v$ is the shortening velocity $($ max of $v_{\text{m}\text{a}\text{x}}),T_o$ is the isometric tension$($ i$.$e$.,$ tension at zero velocity$),$ and $k$ is a non$-$dimensional constant that ranges between $0\mathrm{.}15$ and $0\mathrm{.}25$ for most muscles. The equation can be written in nondimensional form:

$p=ku{T}_o(\frac{1-u}{k+u})$

Where $p=\frac{T**v}{T_o{v}_{\text{m}\text{a}\text{x}}},$ and $u=\frac{v}{v_{\text{m}\text{a}\text{x}}}$

Consider the case for $k=0\mathrm{.}25$

a$)$ Plot $p$ versus $u$ for $0u1,$ use ezplot or fplot command by the given range

b$)$ Use differentiation to find the value of $u$ where $p$ is maximum.

c$)$ Find the maximum value of $p.$ Use the subs command and explain the meaning of the results.