please write the answer as a matlab code or if you can to send it as an matlab file

the course is mechanical vibration lab and just chapter $1$ is allowed

Question $10$

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Consider the following equation of motion of a system and the subjected initial conditions:

$5x^{}+2x^{}+7x=0$

$x(0)=0\mathrm{.}1$ and $x^{}(0)=0\mathrm{.}25$

a$)$ Create a function and find the solution of the equation of motion using ode$45$ for $t$ between $0$ and $50$ sec with an increment of $0\mathrm{.}1.$

b$)$ Plot the displacement $x(t).$ Add the titles for the axis and the graph.

c$)$ Open a new figure and plot the velocity $v(t).$ Add the titles for the axis and the graph.

d$)$ If the equation of motion changed to be:

$7x^{}+4x^{}+3x=0$

$x(0)=0$ and $x^{}(0)=0\mathrm{.}15$

Create a new function and find the solution of the new equation of motion using ode$45$ for $t$ between $0$ and $50$ sec with an increment of $0\mathrm{.}1.$

e$)$ Open a new figure and plot the displacements of the two equations $x(t)$ and $x1(t)$ on the same graph. Add the titles for the axis and the graph and add a legend.

f$)$ Open a new figure and using subplot, plot the displacements and velocities of the two equations such that the first row contains the plots of the displacements $x(t)$ and $x1(t)$ and the second row contains the velocities $v(t)$ and $v1(t).$ Add the titles for the axis and the graph for each plot.