$(40\%)$ The system shown in Figure $3$ consists of two bars, each of bending stiffness

$EI$ elastically hinged together at B by a rotational spring of stiffness $K.$ Regard A and

C as simple pin$-$joints.

$($a$)$ Show that the buckling load of the system is given by the implicit expression:

$P_{cr}=2\frac{K}{tanL}$

$($b$)$ Find the buckling load as $K.$ Explain your result using a physical model.

$($c$)$ Find the buckling load as $EI.$ Explain your result using a physical model.