please solve this without using Ai. the subject is system dynamics and control

Coupled Mass-Spring-Damper System Objective: The objective of this project is to model and simulate the dynamic behavior of a coupled mass-spring-damper system as shown in the figure using MATLAB Simulink. System Description: Consider the coupled system consisting of two masses ( m1 and m2), each mass connected through a spring-damper couple, (k1,b1) and (k2,b2) to fixed walls. Mass m2 is moving under the effect of gravity. The two masses are also connected through a spring k3 which couples their motion. The input, u(t), is a step function. The goal is to analyze the motion of the masses under different conditions. Group Work: Project reports are to be submitted for groups of exactly two students. Important Note: You are expected to use typesetting software such as Word or LaTeX. Handwritten submissions will not receive any credit. You are encouraged to use Overleaf collaborative document preparation in LaTeX on cloud. Project Components: In your work, complete the following steps: 1. Mathematical Modeling: Draw the free body diagrams for each mass showing forces and positions clearly. Derive the equations of motion for the coupled mass-spring-damper system. Represent the system dynamics as i. differential equations, ii. transfer functions (outputs are positions)