a) For each of the following systems, find the two differential equations of motion. Assume the spring forces are proportional to the relative displacements of the masses and the damper forces are proportional to their relative velocities. The displacements $x_1(t)$ and $x_2(t)$ are the output for all the systems. Neglect friction.
i. System #1 in Figure 3 shows the forces $f_1(t)$ and $f_2(t)$ are the system input. The spring of stiffness $k$ is unstretched when $x_1 = x_2$. (CO2, PO2, C4)
ii. System #2 in Figure 4 shows the displacement $y(t)$ and the force $f(t)$ are the system input. The spring of stiffness $k_1$ is unstretched when $x_1 = y$, and the spring of stiffness $k_2$ is unstretched when $x_1 = x_2$. (CO2, PO2, C4)
