Wow. That's quite a lot of RAM to be starved like that. I've been running four moderately-traffic'd Rails apps, along with a smattering of PHP apps, on one "droplet" with (I had to go look at the control panel) 1GB RAM and 30GB SSD. It's been up and running for four years. There's a Rails 3.2 app, a Rails 4.0 app, a Rails 4.2 app, and a Rails 5.1 app. There's also two major PHP apps that get a lot of love from mostly spammers, and one minor one that never gets any traffic. I'm not holding this up as a bastion of good devops, but just to give you the counterpoint that your server is probably not your problem.
What application server are you using, and which database? I'm on Passenger (mod_passenger compiled into Apache), using MySQL.