Finding transfer function of DC motor
You've badly misunderstood the 331. What you are seeing is a single pulse from the current source, rather than a filtered voltage level. The biggest clue is the fact that your pulse is about 100 usec wide. Do you really think a motor shaft will get up to speed in 0.1 msec?

If you look at the data sheet, Figure 19 (which I think you've done to get the circuit), you'll notice that you've omitted a leaky integrator on the voltage output, and replaced it by a simple RC filter. Problem is, a 100 pF cap and a 100k resistor have a time constant of 10 usec, which is roughly what you're seeing on the exponential decay.

So what you need to do is examine your encoder and figure out the frequency you expect to be seeing when the motor is running at its expected speed. You can do this the easy way by applying voltage and looking at the encoder output on your scope.

Then set the RC product of your output filter (R4/C2) at about 1/10 the period of your expected frequency.

With a simple F/V converter like the LM331, you may have a problem making a tradeoff of the output filter, between it being fast enough to accurately show the rise in speed vs. being slow enough to properly filter the current pulses coming out of the converter.

At any rate, your scope should be looking at a time scale on the order of 0.1 to 1 seconds, rather than 0.1 msec. Motors just don't accelerate all that fast.

You should also (unless you're running the motor at really amazing speeds) put as many holes in your encoder disk as possible, so as to get the encoder frequency as high as possible and make your filter's job easier. For instance, if your motor rpm is 1000, and you have 10 holes in your disk, you'll only have an encoder frequency of $$f = \frac{(10\times 1000)}{60} = 167 \text{Hz}$$ and even at maximum speed your update rate for the F/V converter will be about 6 msec for a perfect converter. With an LM331 the effective update rate will be much worse, since the output filter will need to be at least 10 times slower in order to properly smooth the current pulses. This means settling times of the filter on the order of 60 msec.