Q$3$

$(6$ pts$)$ Use a linear system to solve for the displacement of each mass in the illustration. Let

$k=10\frac{(kg)}{s^2}$ and $g=9\mathrm{.}81\frac{(m)}{s^2}$

a Write a system of equations for the illustrated masses and springs. Hint: Sum forces in the ver$-$

tical direction for each mass, $m_i($where $i=1$dots$3).$ A system of $3$ equations $($force balance$)$ and

$3$ unknowns $($displacement of each mass$)$ will result.

b Convert the system into the standard $($i$.$e$.$ natural$)$ form $Ax=b.$

Clearly list all entries of matrix $A,$ vector $x,$ and vector $b$ as numbers $($No unit$)$

Note: You do NOT need to solve this linear system.

Use $m_1=2kg,m_2=3kg,$ and $m_3=2\mathrm{.}5kg.$