Question

1. Figure 1 shows a dynamic vibration absorber, which is used in many applications involving n the vibration of machines with unbalanced components. Obtain the differential equations niido nolvto work describing the system k ON TM (0)d MY k2 howien Isnoaleug My y2 noi nutetens brit 9Tugi worla metayaeds to (2), N(2),V Figure 1. Diagram of a vibration absorber Find the transfer functions relating Xo(s) and Xin (s) for the systems shown in Figure 2 and 2. Figure 3. Xin Xin b: by k M1 noo ai ole bns at g nworle r rtT etave er to (2)NChE=C by Figure 2 Figure 3

Answer 1

1. For mass M1 we can write the differential equation as,

M1 fky1- bj1- k2(y1 -y2)

M1(k+k2)y1b- kyi = f

For the second mass M2, we can write the differential equation as,

-k2(y2-y1) M2j2

M22k2y2 - k2y1 = 0

The above two differential equations describe the system.