civil engineernig question :$-$

A machine is mounted at the centre of a simple supported beam that can exert a harmonic load

$F(t)=20sin(0\mathrm{.}12t)kN$ in vertical direction. The length of beam is $4m$ and its cross$-$section is

uniform throughout. Cross$-$section of beam : width $20mm$ and depth $40mm.$ A weight $W=200$

$N$ is suspended from the centre of the beam by a spring of spring constant $K_s=40\frac{N}{m}.$ Determine

the natural frequency of the weight $W.$ Neglect mass of the beam and weight of machine. $E=2{10}^5$

MPa.