Suppose a signal from a vibrating motor is to be sampled discretely with a digital data acquisition system to determine the RPM of the motor. It is known that the maximum possible RPM is 1800. What is the minimum sampling frequency (in Hz) with which the signal can be sampled in order to measure the RPM of the motor? For full credit, show all your work and explain.

For the same conditions as above, suppose also that the RPM needs to be known to a resolution of 2 RPM (±1 RPM). Calculate the minimum number of discretely sampled data points necessary to achieve this resolution.