What knot(s) should I use to secure this?

counselwolf@lemmy.world to No Stupid Questions@lemmy.world – 51 points –

The yellow arrow points to a leather cord tied similar to a poacher's knot to have an end loop.

The red arrow are ends of an elastic string which passes through a hole (one for each end) in the leather.

I need to tie the elastic string ends in such a way to secure both the leather cord, and on itself so that when the elastic is pulled, it will not stretch. Also it should be hard but not impossible to untie.

Also it should not be too bulky.

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A flat overhand bend in the elastic cord is what I recommend: https://www.animatedknots.com/flat-overhand-bend-knot

Justification:
Simple, not bulky, reasonably secure against shaking loose, and relatively easy to untie.

As suggested in another comment, a double figure eight could be used as well. It will be more bulky and a bit less likely to come loose.

would I be able to cut the ends and it won't come loose?

If you want to be able to trim off the ends, I suggest a double fisherman's instead (aka the double overhand stopper) with both strands (hold them together while you tie and treat them as a single strand).

https://www.animatedknots.com/double-overhand-stopper-knot

With either knot, after you trim, you can melt the ends of the elastic cord. It will "mushroom" a bit, which will also prevent the tips from creeping into the knot and coming loose.