I am to perform an experiment on frequency modulation. And one of the objectives of the experiment is 'to investigate the time response of FM'.
In the experiment, a variable amplitude constant frequency sinusoid (modulating signal) is applied to an FM modulator and the output of the modulator is observed with the help of an oscilloscope and a frequency counter. Then the expt is repeated with a constant amplitude but variable frequency sinusoid and the results are compared.
There are only two 'time response' actions of interest in this type circuit.
Time delays in modulator output with response to input change. delay when change starts and 'settle' time when changing input becomes constant again. There are many ways to measure the errors and their rate of occurance depending on what you are investigating and how it pertains to your problem.
(Slew rate measurements when used with square wave inputs could be considered as well.)