Exercise $1$: Modeling of a second order system

Construct a Simulink diagram to calculate the response of the Mass$-$Spring system. The input force increases from $0$ to $8$ N at $t=1s.$ The parameter values are $M=2kg,K=16\frac{N}{m},$ and $B=4N.\frac{s}{m}.$

Steps:

Draw the free body diagram.

Write the modeling equation from the free body diagram.

Solve the equations for the highest derivative of the output.

Draw a block diagram to represent this equation.

Draw the corresponding Simulink diagram.

Use Step block to provide the input fa$($t$).$

In the Step block, set the initial and final values and the time at which the step occurs.

Use the $"$To Workspace" blocks for $t,F_a(t),x,$ and $v$ in order to allow MATLAB to plot the desired responses. Set the save format to array in block parameters.

Select the duration of the simulation to be $10$ seconds from the Simulation $>$ Parameters entry on the toolbar.

Given below is a file that will set up the MATLAB workspace by establishing the values of the parameters needed for the Simulink simulation of the given model.