Q$3.$ The force acting on the work$-$piece of the forging hammer shown in fig $1.$ due to impact by hammer can be approximated as rectangular pulse as shown in fig$2.$ Find the resulting vibration of the system for the following data: mass of the work piece, anvil and frame $(m1)=200kg,$ mass of the foundation block $(m2)=250kg,$ stiffness of the elastic pad$($k$1)=150\frac{N}{m},$ and stiffness of the soil$($k$2)=75$ N$/$m$.$ Assume the initial displacements and initial velocities of the masses as zero

Fig $1$

Fig $2$