Problem $2$: Consider the mechanical

system above where:

$2N\frac{s}{m},b_2=6N\frac{s}{m},k_1=50\frac{N}{m},$

$k_2=40\frac{N}{m},k_3=46\frac{N}{m})$ with

initial condition $x(0)=1m$ and

$x^{}(0)=2\frac{m}{s}.$

Derive the equation of motion for the system above.