Constructing The Model
According to Newton's second law of motion, the force $F$ is related to the mass $m$ and acceleration $a:$ $$F=ma$$ Since the acceleration is the rate of change of velocity, by using the above equation, we have $$a={d}/{dt}({dx}/ {dt}) = {d^2x}/ {dt^2}={1}/{m} F $$ So, once we know the external force $F$ and mass $m,$ we can use the above equation to calculate the acceleration $a$. Now, as differentiation and integration are inverse processes, it is straightforward to notice that we can obtain our desired velocity ${dx}/ {dt}$ and position $x$ simply by applying integration operation twice on the acceleration $a$ since $a={d^2x}/ {dt^2}.$ Simulink provides us with an integration operation block called integrator to perform this task easily (see the picture below).
