$2\mathrm{.}16$ A two$-$mass translational mechanical system has the following mathematical model:

$m_1{x}_1^{}+b_1{x}_1^{}+k_1(x_1-x_2)=f_a(t)$

$m_2{x}_2^{}+b_2{x}_2^{}+k_1(x_2-x_1)+k_2{x}_2=0$

The displacements $x_1$ and $x_2$ are measured from their respective equilibrium positions. An external

force $f_a(t)$ is applied to the system. Sketch a possible configuration of the two$-$mass mechanical

system. Label all elements and show the positive convention for displacements on your sketch.

Sketch the FBDs for each mass and verify the system model by applying Newton's laws.

$2\mathrm{.}17$ Repeat Problem $2\mathrm{.}16$ if the mechanical model of thetwo$-$mass translational system is

$m_1{x}_1^{}+k_1{x}_1+k_2(x_1-x_2)=0$

$m_2{x}_2^{}+k_2(x_2-x_1)=0$

$2\mathrm{.}16$

FBD:

$\{\begin{array}{c}\text{:}{k}_1(x_2-x_1)(m_2^{x_2}){\displaystyle \underset{F}{\overset{\phantom{}}{}}}{?}_{m_2{x}_2^{}}larr{k}_2{x}_2^{}\end{array}$

Ive already worked $2\mathrm{.}16$ i need $2\mathrm{.}17$