Full range speaker directly connected to amplifier

My Kenwood speakers 2 way tweeter has inline capasitor 3.3uf and twetter is connected to woofer in parallel and woofer is directly connected to amplifier do we need some capasitor or something as no crossover is in it when on full volume it distorts some times
 
If it distorts in the bass, there is no help with a filter. Usually a bass driver is cut off from treble by a inductor. Either your amp is clipping (overloaded) or the speaker bass driver is pushed to hard (to high level).

Time for an upgrade?

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that's a good sign with the 100uF cap- lucky as a capacitor's reactance can combine with a driver's impedance peak (s) to exacerbate cone excursion. (a good thing when done on purpose with so-called 3rd order sealed boxes)
 
Pics!! Which Kenwood speaker (s)? From the '70s? '80s?'90s? How big Is the woofer? I suspect it's a 5" woofer and 2"(paper cone) tweeter or even piezo 😉
Which can be considered full range, I Guess...if you play with mechanical cross-over of a physical device like a speaker, which Is not a perfect piston, It Will show (in box)a High pass behavior which is defined by F3 at low frequency and Fc at treble Is found when break-up issue of the membrane Is negligible..
 
Woofer is 5.25 inch and tweeter is 2 inch and as mentioned before it's two way system tweeter working great but issue with woofer

Below attached pic of speakers and amplifier specs(orginal)
Also attached tweeter pic with crossover but I have changed it to filim capasitor same value 3.3uf 100v as old one was leaking

Also i am not using same amplifier I bought nobsound ns-20g amplifier
And connected to it
 

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