Problem B$-5-23$

Consider the system shown in Figure $5-45.$ The system is at rest for The displacements $y_1$ and $y_2$ are measured from their respective equilibrium positions before the input force $u$ is given at $t=0.$ Obtain a state$-$space representation of the system.

rigure $5-45$ Mechanical system.

Assuming that $m_1=10kg,m_2=5kg,b=10N-\frac{s}{m},k_1=40\frac{N}{m},$ and $k_2=20\frac{N}{m}$ and that input force $u$ is a constant force of $5$ N $,$ obtain the response of the system. Plot the response curves $y_1(t)$ versus $t$ and $y_2(t)$ versus $t$ with MATLAB.