For the structural system shown below, evaluate the i$)$ effective stiffness, ii$)$ natural frequency and natural period; given that the length of cantilever L $4$m$,$ modulus of elasticity of cantilever E$-22000$ MPa, second moment of area I $=1\mathrm{.}5$x $10$ m$^2,$ stiffness of springs k $=35$ kN$/$m$,$ and mass m $9\mathrm{.}8$ kN$.$ If the initial displacement is $30$ mm and the initial velocity is $25$ mm$,$ iii$)$ write the equation of motion of the system, iv$)$ compute the maximum amplitude of motion, and v$)$ compute the amplitude of motion after $1$s$.$