Electronic – Negative resistance circuit

There are several points in the AD843 datasheet that appear to be relevant.

I first spotted the "Overdrive Recovery" time (under the general category of "Frequency Response"). Note that the recovery time for positive overdrive (found in your negative peak detector) is significantly longer than the recovery time for negative overdrive (found in your positive peak detector). Half a microsecond when your pulse width is on the order of 2.5 µs (half-cycle @ 200 kHz) could be significant.

Second, the datasheet specifically mentions that the AD843 has trouble driving capacitive loads. Your 10 nF capacitor is more than an order of magnitude larger than any example load they mention in the datasheet.

Third, there is a peak detector circuit given in the datasheet. The topology is slightly different from yours, but more significantly, they use the AD843 in the output stage, but use an AD847 in the input stage "since the AD847 can drive an arbitrarily large value of capacitance".

From the topology you can see this is a low pass filter. I would start with getting some intuition of how this filter is going to behave, rather than trying to see what exactly happens at your frequency. For frequencies well below the rolloff, you can approximate the capacitor as a open, and well above the rolloff as a short. By computing the gain at the limits and looking at where the rolloff frequency is, you can draw out a Bode plot from inspection.

Then you can look at where your frequency of interest fits on that plot and get a quick idea of the gain.

That brings up another issue, which is that it's unclear what your frequency is since you haven't defined the units of T. If T is in seconds, then the frequency is 1000 / (2π s) = 160 Hz.