The system shown below obeys the differential equation i.e., Input-Output model).

\[\left(m_{1}+m_{2}ight) \ddot{x}+\left(b_{1}+b_{2}ight) \dot{x}+k x=f(t)-m_{2} g,\]

where \(x_{1}=x_{2}=x\).

(a) Verify that the differential equation is correct.

(b) Find the expressions for the damping coefficient \(\xi\) and the undamped natural frequency \(\omega_{n}\).

(c) Find the steady-state response when the force is a step unit function.

Transcribed Image Text:

f(t)- mi b XXXXX k 000 Ideal pulley m2 x2 k b A Second-Order Translational Mechanical System