helpQUESTION $1$

a$)$ In order to determine the effect of changes in the stiffness of the elements of

bed$/$foundation system of machine, this system is considered as an equivalent spring

model as shown in Figure Q$1($a$).$ Four components of the system are involved. There

are the bed, the concrete, the bed$-$to$-$concrete joint and subsoil. Given the stiffness of

bed, concrete, and subsoil are $22\mathrm{.}2{10}^6\frac{N}{m},24{10}^6\frac{N}{m},$ and $1\mathrm{.}87{10}^9\frac{N}{m}$

respectively. Analyse the suitable stiffness of bed$-$to$-$concrete joint, $k_j$ if the equivalent

stiffness of this system, $k_{eq}$ is $672{10}^6\frac{N}{m}.$

$[15$ Marks$]$

Figure Q$1($a$)$