e single degree of freedom system in figure below:              Make the correct selection: The system above is:

2. Figure 2 shows a roller rolling and slipping at the same time on a slippery surface. The center of the roller moves with a displacement r(t) and the roller rotates with angle (t). The roller has mass m, mass moment of inertia I, and radius r. In addition, a layer of fluid with viscous damping coefficient c is present to lubricate the roller. Moreover, the roller is pulled by a spring under a given (i.e., prescribed) displacement u(t), whereas the spring has spring constant k. Also, the roller is subjected to an applied torque M(t). Figure 3 shows the free-body diagram of the roller. Answer the following questions. (a) Apply F = ma to derive an equation of motion governing the translation z(t). (b) Apply M = Ia to derive an equation of motion governing the rotation 0(t). (c) Eliminate the variable (t) from the two equations of motion derived in parts (a) and (b). You should obtain a third-order differential equation in x(t). (d) Initially (i.e., at t = 0), the roller has no…

Q4-6 please

For the system shown in the figure, set up the equation of motion for the mass, m, and solve for the steady state amplitude and phase angle.