NOTE: You must use if$-$else statement

Project $($I$)$

The objective of this project is to implement a MATLAB script that solves the differential equation

governing damped harmonic motion for a mass$-$spring$-$damper system. The project aims to study

the effects of different equations representing the system under different conditions $($you must

use if$-$else statement$).$

The $8-kg$ body is moved $0\mathrm{.}2$ m to the right of the equilibrium position and released from rest at time

$t=0.$ Using MATLAB, calculate the displacement as a function of time $(t=0$:$0\mathrm{.}1$:$5)$ for three cases,

$c=8,32,$ and $56N.\frac{s}{m}($where c is the damping coefficient$).$ The spring stiffness k is $32\frac{N}{m}.$

Case $($I$)$ : the system is underdamped $c=8$

The initial condition: $x_o=0\mathrm{.}2,x^{}=0,C=0\mathrm{.}207m,=1\mathrm{.}318,{}_d=1\mathrm{.}937$

Case $($II$)$: the system is critically damped $c=32$

The initial condition: $x_0=0\mathrm{.}2,x^{}=0,A_1=0\mathrm{.}2m,A_2=0\mathrm{.}4\frac{m}{s},{}_n=2$

Case $($III$)$ : the system is overdamped $c=56$

The initial condition: $x_o=0\mathrm{.}2,x^{}=0,B_1=0\mathrm{.}222\frac{m}{s},B_2=-0\mathrm{.}0219\frac{m}{s}$