"The only calculation that needs to be made is matching the electric motor to the rated max. output of the pump."
Not quite. Its true for gas powered, not for single phase induction motors. You have to find the RMS horsepower.
Here is a good explanation written by Ed Cowern:
There are a great many applications especially in hydraulics and hydraulically-driven machines that have
greatly fluctuating load requirements. In some cases, the peak loads last for relatively short periods
during the normal cycle of the machine. At first glance, it might seem that a motor would have to be
sized to handle the worst part of the load cycle. For example, if a cycle included a period of time where
18 HP is required, then the natural approach would be to utilize a 20 HP motor. A more practical
approach to these types of “duty cycle loads” takes advantage of an electric motor’s ability to handle
substantial overload conditions as long as the period of overload is relatively short compared to the total
time involved in the cycle.
The method of calculating whether or not the motor will be suitable for a particular cycling application is
called the RMS (root mean squared) horsepower loading method. The calculations required to properly
size a motor for this type of application are relatively simple and are presented in this paper.
The RMS calculations take into account the fact that heat buildup within the motor is very much greater
at a 50% overload than it is under normal operating conditions. Thus, the weighted average horsepower
is what is significant. RMS calculations determine the weighted average horsepower.
In addition to reducing the size and cost of a motor for a particular application, RMS loading also offers
the advantage of being able to improve the overall efficiency and power factor on a duty cycle type of
load. For example, when an oversized motor is operated on a light load, the efficiency is generally fairly
low, so working the motor harder (with a higher average horsepower), will generally result in improved
overall efficiency and reduced operating cost.
The rest of the article is here:
www.motorsanddrives.com/cowern/motorterms9.html
As the saying goes: "You cannot compare an apple to an orange".