Problem $4(13\%$

For the system shown in Fig. Prob. $4,$

$($a$)$ determine the direction angles of $F.$

$($b$)$ calculate the moment of $F$ about the origin, $O.$

$($c$)$ delermine the angle $$ between the force $F$ and

the line $AO.$

Fig. Prob.$($Newton $2$nd Law, assume small rotation, thin rigid beam$)$ For the system shown in Fig. Prob$-2,$ determine the equation of motion in the form m$\_($v$)$v$^()+$c$\_($v$)$v$^()+$k$\_($v$)$v$=$p$\_($v$)($t$)$ where v$($t$)$ is the vertical displacement of end E $.$ Assume small rotation of the thin, rigid, uniform beam AE$,$ whose total mass is M $.$ p$\_(0)$f$($t$)$ per unit length