Problem $8$: For the system shown, $M=1kg$;$K_1=K3=20\frac{N}{m}$;$K_2=10\frac{N}{m}$;$K4=15\frac{N}{m}$;$B1=4N-\frac{s}{m}$; $B2=3N-\frac{s}{m}$;$B3=5N-\frac{s}{m}$;$B4=1N-\frac{s}{m}$

$8$a$)$ Find Beq and Keq for the system: The springs have zero stored energy when $x=0.$

$8$b$)$ MATLAB Coding: Using "ode$45",$ plot displacement $x$ and velocity v versus time graph for $0t10$ seconds when subjected to $f_a(t)=e^{-t}sin(t).$ Note: Initial Conditions $($I$.$C$.)=0.$ Refer MATLAB manual for a similar example $($example $3$ on page $6).$