A solid homogeneous cylinder of radius 'r' rolls without slipping on the inside of a stationary large cylinder of radius 'R' the period of small oscillations about the stable equilibrium position is-- (2(R-r)' 2n 3g 3g V \2(R-r)) (3(R-r)` 2g 2g (3(R-r).

(III) A mass m is connected to two springs, with spring constants k1 and k2, in two different ways as shown in Fig. 14-32a and b. Show that the period for the configura- tion shown in part (a) is given by 1 1 T = 2 %3D m k2. and for that in part (b) is given by m T = 2T %3D V k1 + k2 Ignore friction. vig www.wiw- k1 k2 m (a) k1 k2 w ww w ww m FIGURE 14-32 Problem 25. (b)

A uniform annular ring of mass m and inner and outer radil a and b, respectively, is pivoted around an axis perpendicular to the plane of the ng at point P (see figurm bet). Detemine ts penod sf cscillation. (Use the following as necessary: m, a, b, and g for acceleration due to gravity) T-

#3