How to make a passive linear circuit to generate high voltage spikes from 10V peaktopeak square wave with a source res. of 50Ω, with f less than 5MHz
If you use passive devices, you're essentially limited to RLC (and some other things like diodes). Here are ways you can implement the different parts of the design. It sounds like a homework assignment, so I'll at least point you to some resources that you can assemble and test in LTspice.
First, there's a discrepancy between the input voltage and the output voltage. If you can only use passive devices, you can use some kind of voltage multiplier: https://www.electronics-tutorials.ws/blog/voltage-multiplier-circuit.html Those examples will turn your 10 V square wave in to 30 V, recharging every cycle.
Once you have a capacitor charged up to 30ish V, you can discharge that capacitor to generate a pulse. As long as you have input square waves coming in, the capacitor will charge, and you can discharge it again. The values of C and R can then be chosen to get the right pulse width and output impedance.
As a side note: I accidentally made one of these pulse sources while trying to make a super-fast PTT for radio digital modes. If the discharge time is too fast, it just pulses every period of the input wave. Slow down the discharge time, and it will just hold a mostly constant voltage as long as your square wave source is on. In my case, I fed that in to a transistor switch, but in your case, that will be your output.