Question $1.$

Idealized spring$-$mass systems have numerous applications throughout engineering. Figure below shows an arrangement of four springs in series being depressed with a force of $2000$ kg $.$ At equilibrium, forcebalance equations can be developed defining the interrelationships between the springs.

$k_2(x_2-x_1)=k_1{x}_1$

$k_3(x_3-x_2)=k_2(x_2-x_1)$

$k_4(x_4-x_3)=k_3(x_3-x_2)$

$F=k_4(x_4-x_3)$

where the k$\text{'}$s are spring constants. If $k_1$ through $k_4$ are $150,50,75,$ and $225\frac{N}{m}$ respectively, compute the $x\text{'}$s by Matlab capability to solve system of linear algebrai equations. Obtain first the A matrix and B RHS vector. Solve using X $=$ A B $.$

Create a Livescript with the sequence of instructions to solve the problem.