Question

Question 2 (Combinatorial system). For the system shown in Figure 2, the disk rolls without slipping, the masses of the pulleys are negligible, and the cable is inextensible. The coordinates are defined relative to the static equilibrium position of the system. Derive the equation of motion in terms of y (mass position). X WWW Figure 2: Rotational / translational system.

Answer 1

M2 m. FOR the disc And AISO pulley is movable So, as x distance Robe move Speed + Fox distance x the s disc Rotales e Angle pulley moves Y= * distanc e Speed - equation of Enexgy Method To find Use Now - We System Motion of System = k of Total K.E. energy Toanslation Rotational KE of KE. of mass Ma MASS Mars Moment of inestia of disce N Неве,

mg Potential Energy of System, U = Total %3D [Re=x} =) Knowe that totel Enegay of System Remains Constant Aluways We Total Energy Total Total Constant Kinetic Petenticl Enegy Energy ma

we get fime Dittesentiating g -O L0.8.+ Speed lvelocity is Diffesentiation of 4 w.8+ t where ý: dy : Accelexation di Differentiation of W.8.t. $. d m, So 4ky (amy + mil ÿ + 4ky equation of Civen System. This Motion is