For the spring assemblage shown in Figure,

$($a$)$ determine the displacement at node $2$

$($b$)$ the forces in each spring element, and

$($c$)$ determine the force F$3.$

Given: Node $3$ displaces an amount $=1$ in$.$ in the positive $x$ direction because of the force F$3$

and $k1=k2=1000l\frac{b}{i}n.$

For the spring assemblage shown in figure, obtain

$($a$)$ the global stiffness matrix by direct superposition,

$($b$)$ If nodes $1$ and $5$ are fixed and a force $P$ is applied at node $3,$ determine the nodal displacements,

$($c$)$ determine the reactions at the fixed nodes $1$ and $5.$