$2\mathrm{.}10$ A two$-$mass transfational mechanical system has the following mathematical model:

$m_1{x}_1^{}+b(x_1^{}-x_2^{})+(k_1+k_2)x_1-k_1{x}_2=0$

$m_2{x}_2^{}+b(x_2^{}-x_1^{})+k_1(x_2-x_1)=f_a(t)$

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.