MCH $3008$ PROJECT $1\mathrm{.}1$

Question $1$: In the following figure the force $F(t)$ is applied to the mass $m_2$ and another mass $m_1$ connected to it$.$ The spring with the stiffness coefficient $k_2$ and the damper with damping coefficient $b_2$ model the coupling between the two objects. The spring with the stiffness coefficient $k_1$ and the damper with damping coefficient $b_1$ model the coupling between the object and the wall. Take $m_1=m_2=b_1=b_2=k_1=k_2=1.$

a$)$ Write the equations of motion of this system.

b$)$ Find the transfer function between $F(t)$ and $y_1.$

c$)$ Assume that $F(t)=1$ is applied to the system at $0t10.$ Simulate this system with a MATLAB program and Simulink model using a transfer function approach. Plot the $u(t)$ and $y_1(t)$ curves.

d$)$ Obtain the state space model. Assume again that $F(t)=1$ is applied to the system at $0t10.$ Simulate this system with a MATLAB program and Simulink model using a statespace approach. Plot the $u(t)$ and $y_1(t)$ curves. can you guys help me with the mathlab partss