Can someone show me step by step with all work shown to solve this question? Thank you

Trans$-$mitral flow velocity profile based on the simple harmonic oscillator model is given by;

$v_E(t)=\frac{x_{0}k}{m}{e}^{-t}sin({}_{E}t),=\frac{c}{2m},{}_E=\frac{\sqrt[\phantom{2}]{4mk-c^2}}{2m}$ for the E$-$wave and

$v_A(t)=\frac{F_0}{2}(-t{e}^{-{}_{a}t}+\frac{sin({}_{a}t)}{{}_a}),$ for the A$-$wave.

Parameters are given by;

$x_0=11\mathrm{.}96,c=18\mathrm{.}43,k=256\mathrm{.}13,m=1$ for the E$-$wave and

$F_0=4593,{}_a=23\mathrm{.}49$ for the A$-$wave.

Velocities are in $(c\frac{m}{sec}).$

a$.$ Plot the E$-$ and A$-$wave profiles, and calculate the E$/$A ratio. Plot the velocity profiles

from $t=0$ to $t=\frac{}{{}_E}$ for the E $-$wave and $t=0$ to $t=\frac{}{{}_a}$ for the A$-$wave.

b$.$ Increase the damping coefficient, $c$ by $1\mathrm{.}5$ times, and decrease $x_0$ by $0\mathrm{.}8$ times and

repeat a$.$

c$.$ In addition to the changes made in b$,$ increase the stiffness, $k$ by $3$ times, and repeat

a$.$

d$.$ In addition to the changes made in b$,$ increase the stiffness, $k$ by $4$ times, and

decrease $F_0$ by $0\mathrm{.}8$ times, and repeat a$.$

e$.$ Discuss what pathological conditions can change $x_0,k,c,$ and $F_0,$ and their effects

on the E$/$A ratio based on the above results.