Question 1 (20 pts)The passive mechanical behavior of skeletal muscle is modeled using a linear spring $k_1$ in series with a parallel linear spring-dashpot combination $k_2, b$.System Setup: One end of the muscle is fixed; the displacement of the other end is $x$.Definitions: If $x_1$ is the change in length of $k_1$, the forces are $F_1, F_2,$ and $F_b$, where $x_2 = x - x_1$.(a) If length $x$ is stepped and held from $0$ to $X_0$ at $t = 0$, solve for the applied force $F$.(b) If force $F$ is suddenly stepped and held from $0$ to $F_m$ at $t = 0$, solve for the change in length $x$.Question 2 (30 pts)A two-compartment model of glucose-insulin kinetics. $I_p(t)$ is intravenous insulin, $I$ is insulin in a remote compartment, and $G$ is glucose concentration in plasma.+1Model Parameters:| Parameter | Value | Parameter | Value || :--- | :--- | :--- | :--- || $k_1$ | $0.015 \text{ min}^{-1}$ | $k_5$ | $0.035 \text{ min}^{-1}$ || $k_2$ | $1 \text{ min}^{-1}$ | $k_6$ | $0.02 \text{ mM}^{-1}\text{min}^{-1}$ || $k_3$ | $0.09 \text{ min}^{-1}$ | $B_0$ | $0.5 \text{ mM min}^{-1}$ || $k_4$ | $0.01 \text{ mM}^{-1}\text{min}^{-1}$ | | |Input: $I_p(t) = 200 \text{ mM}$ for $0 \le t < 0.1 \text{ min}$, and $0$ otherwise. Initial Conditions: At $t = 0$, $I = 0$ and $G = 10 \text{ mM}$.Task: Solve for $I$ and $G$ using MATLAB for $0 \le t \le 60 \text{ min}$.Question 3 (40 pts)A three-element model of active cardiac muscle contraction. Total tension is $T = T_p + T_s$.+1Governing Equations $T_p = \beta(e^{\alpha(L-L_0)} - 1)$$T_s = \beta(e^{\alpha L_s} - 1)$$\frac{dL_c}{dt} = \frac{a[T_s - S_0f(t)]}{T_s + \gamma S_0}$Activation Function:$f(t) = \sin(\frac{\pi}{2}[\frac{t+t_0}{t_{ip}+t_0}])$ for $0 \le t < 2t_{ip} + t_0$, else $0$.Constants17:$L_0 = 10 \text{ mm}$, $\alpha = 15 \text{ mm}^{-1}$, $\beta = 5 \text{ mN}$, $S_0 = 4 \text{ mN}$, $\gamma = 0.45$, $t_0 = 0.05 \text{ s}$, $t_{ip} = 0.2 \text{ s}$.(a) Use Python to solve/plot $T$ vs time for an isometric contraction ($L = L_0$).(b) Solve/plot length $L$ vs time for an isotonic contraction ($T = 0$).Question 4 (10 pts)A left ventricle is modeled as a spherical shell with inner radius $A$ and outer radius $B$. It expands to new radii $a$ and $b$. Assuming the myocardium is incompressible, find $b$ as a function of $a, A,$ and $B$