Your question needs a lot of work. No voltage scale, no time scale, and the pulses are so narrow that they convey almost zero information. AND - why do you think this circuit works at all? Please explain why you think you need a 10 meg resistor in a feedback loop, and why neither end of the signal generator is grounded.
Both of your opamp circuits are a form of a linear amplifier. As such, there is no one element that can be changed to turn it into a pulse form circuit. You need a different circuit.
If you want the leading edge of the input signal to initiate an output pulse of some independent width, that circuit is called a monostable multivibrator. This can be done with an opamp, a comparator, two digital logic gates, or a digital logic part designed specifically for this. A search for monostable schematic or monostable circuit will bring up hundreds (thousands?) of examples.
Is this school work, or work-related?