The punch press can be modeled as a three$-$degree$-$of$-$freedom system for vibration analysis in the vertical direction. The tool$-$base mass $(m_1)$ is subjected to an impact load $f(t)=1000(t).$ The system is initially at rest.

Parameters: $m_1=400kg,m_2=2,000kg,m_3=8,000kg,$

$k_1=300,000\frac{N}{m},k_2=80,000\frac{N}{m},k_3=8,000,000\frac{N}{m}$

Ignore the dampers in the diagram.

Find the response of the system due to the impact using the modal analysis technique.

Submic:

A cover page.

Problem statement $($short description$).$

Derivations including the free$-$body diagrams, equations of motion, mass and stiffness matrices, and the modal analysis process $($this is the process of decoupling the equations of motion. See lecture notes.$)$

Matlab computer program.

Three plots: $x_1(t),x_2(t)$ and $x_3(t)$ as functions of time in separate plots. Choose the time span from $0$ to $10$ seconds. Plots must have labels with proper units and large enough font size.

A short discussion on what you have learned from solving this problem.

Part $3)$ can be hand$-$written. The writing must be neat and the plots should be clearly labeled. All discussions need to be typed in Word. Combine all parts into one PDF file for the submission.