A motor is mounted solidly on a rigid table, and the table is sitting on some isolation mounts as shown. The acceleration versus time graph shown below was collected when an impulsive force is applied vertically on the table with the motor turned off. When the motor is running at steady state, the accelerometer recorded a signal with amplitude of 4.0 m/s^2 and 11.0 Hz. It has been determined that this oscillation is caused by an unbalanced force within the motor itself, not from other sources on the floor. (a) Determine the natural frequency of the system. (b) Determine the system oscillation amplitude, X [meters], when the motor is running at steady state. (c) When the motor is running at steady state, if X is to be reduced by 50%, calculate the possible frequency ratio, r, required to achieve this reduction in X. To simplify the design, assume the stiffness K and the damping factor of the system will stay the same. There is no need to find the new M. _ccelerometer Motor Table Floor Acceleration (1251 SR 9.81 m/s) 250 215 200 173 148 150- 100 50 0 Machine Impulse Response T = 0.1 sec Time (s)