Fig. Q1 shows an inverted pendulum consisting of a spherical ball of radius R and mass m and a uniform rod of mass my and length a. Pendulum is pivoted at O. Two springs, each of stiffness k, are attached to the ball as shown in the figure. Determine the equation of motion and derive an expression for the natural frequency of vibrations of the system. Take the moment of inertia of a sphere about its centre as mr, where m is the mass and r is the 5 radius of the sphere. m a If m = m, m = and R. show that the natural frequency oo, is approximately given 5 4 by 00=0.438 25 3 m a What is the condition for stability of the system? m! mi B anton Fig. Q1 m