!!~!!~!!

P2.2 A dynamic vibration absorber is shown in Figure P2.2. This system is representative of many situations involving the vibration of machines containing unbalanced components. The parameters M2 and k12 may be chosen so that the main mass M1 does not vibrate in the steady state when F(t) = a sin(ω0t). Obtain the differential equations describing the system.

ki Force F(t) Mi Tro k12 M2 y2(t) FIGURE P2.2 Vibration absorber.