A foundation for well$-$adjusted single acting drop hammer is situated on a compacted sand

deposit. Details of machine foundation and soil are given below

Weight of tup $=20kN$; Height of fall of tup $=1\mathrm{.}5m$

Weight of stand $=40kN($stand is connected to the anvil$)$

Weight of foundation $=5$ times the weight of Anvil

Weight of anvil $=55kN$; Area of anvil $=1\mathrm{.}5m^2$

Thickness of pad below anvil $=0\mathrm{.}12m$

Elastic modulus of pad material $=260$MPa

Area of foundation: $8$ times the area of anvil

Shear modulus of soil $(G)=260M\frac{N}{m^2}$; Poisson's ratio $()=0\mathrm{.}33$

Co$-$efficient of restitution $(e)=0\mathrm{.}50$

Find out $($i$)$ Natural frequencies of the system, $($ii$)$ Amplitudes of the foundation and anvil,

$($iii$)$ Stress on elastic pad, and $($iv$)$ Stress on soil.