A circular cylinder of mass m and radius r' is connected by a spring of stiffness k as shown in the Fig. (b). If it is free to roll on the rough horizontal surface without slipping, find its natural frequency using energy method. (CLOI, PLOI) (b) (13%) For the free vibration of a SDOF system as shown in the Fig. (c), the amplitudes 1.403 mm & 1.326 mm are measured at 1.242 s & 12.734 s, respectively. The number of cycles of oscillation can be noted from the Fig (c). Find the un-damped natural frequency wn and the damping ratio . in www Fig. (b) A circular cylinder connected with a spring Displacement, x (in mm) 1.5 1 0.5 0 -0.5 7 -1.5 -2 0 1.400 2 6 4 8 Time, 1(s) Fig. (c): Measured free vibration of a damped Spring-mass system. 10 12 14 326 16 18