(Solved): Please complete for the shown diagram. PLEASE POST MATLAB CODE TOO. For each of the following MDO ...

Please complete for the shown diagram. PLEASE POST MATLAB CODE TOO.

For each of the following MDOF mechanical systems (see last page), complete the following steps: Find the governing equations using free-body diagrams and Newton's laws \( { }^{1} \). SHOW YOUR WORK. Also use the following assumptions: - No gravity. - Configuration shown is the datum (zero) reference; all springs undeformed at that point. - Use the coordinates given. Put the equations in vector first order (state variable) form and use MATLAB to find the response to a \( 1 \mathrm{~N} \) step input using STEP. Use the following assumptions in all problems: - Input \( u(t) \) is a force acting as shown. (STEP will set \( u(t)=1 \) at time \( t=0 \) ) - Output \( y(t) \) is the position of mass \( m_{1} \). - Use the following parameters, as applicable: c. On problems B and D, also complete the following: - Find the stiffness matrix. Check to ensure that it is symmetric and that the main diagonal elements are all positive. - Plot the system poles (roots of the characteristic equation) in the complex plane using PZMAP. Ensure that they are all on the imaginary axis (to within roundoff error). d. On all problems, print out the pole locations and their damping ratios using DAMP. B. \( \frac{1}{k} 1 \frac{1}{1 / 3} 1 \) \( \psi_{1}+m_{1} k_{3} \) \( x_{2}+1 m_{2} \) \( k_{4} \frac{1}{1 !} \mid v \omega_{1} \)