Write out the $($relevant$)$ equations of motion for the system shown in Figure $3$ below when:

$($a$)$ A and B are free

$($b$)$ A is clamped

$(8)$

$(7)$

$[15]$

Figure $3$

sA and sc are spring constants. Assume A moves along the line of the springs. Note: You do not have to solve these equations of motion.