2003 Hyundai Elantra Suspension

Hello!

I have just purchased a used 2003 Elantra w/98k miles. I've noticed that the car seems to feel unstable/tossed around a bit on the road, sort of left to right as opposed to up and down; it doesn't feel solid, and I think the struts need replaced. Could you describe what it would feel like if this were the case?
Just want to confirm my observations.

THank you!