(b) Consider a system where the disk 1s replaced by a block with mass 30 kg. Find the equation of k = 200 N/m motion of the system. Assume that the contact between the block and ground 1s frictionless. A Ans: X = ix () Both systems will show oscillatory motion. Which system (a) or (b) has a higher frequency? Please provide a physical reasoning for your answer (and not based on just the equations). Hint: For a system with an equation of motion mxX + kx = 0, the general solution has the orm x(t) = A cos(wt + ) and the frequency of oscillation is given by, w = X rad/s f quency given b; Problem 7: A uniform disc of mass 30 kg and radius 0.5 m 1s attached to a spring of stiffness / C\\ 200 N/m. The unstretched length of the spring 1s = lo = 1m and the disc rolls without slipping on the ground (note that this means friction exists between the disk and the ground). (a) Find the equation of motion of the disk. The equation of motion should only involve the variable x and its derivatives. Note that 8 can be taken to be 0 when the spring was unstretched. e 2 k Ans: x = =x 3m