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I recently purchased a 1989 C4 Coupe.
It rides like a chuck wagon. Is it time to replace the springs?
Does this year have composite springs in it. Is it worth the time replacing them?
I put new KYB shocks on it, rides a little better.
The C4 Corvettes have composite springs in them and don't really "wear out". They can become damaged, but even that is uncommon, but still possible.
Due to the C4 being designed as a T-Top car and last minute being changed to a Targa Top there are some last minute changes that were done to keep the frame rigid. These changes supposedly resulted in a harsher ride than originally planned (and make it a bear to get in and out of the vehicle).
They are very rough riding vehicles, but they did get softer over the years. With an 89 your car is closer to the harsh ride the 84 had, but is still softer than earlier models.
Unless your car has very unpredictable handling or you hear metal banging I wouldn't worry too much. It is worth a look at bushings to see how worn they are. If they're crumbling or just about gone, it isn't too hard of a job to change them with a press or even a vice and a bit of ingenuity in either end.
Experiment with lower tire pressures. I started running my 89 with new tires at 35 PSI and slowly started dropping and now am quite happy at 30. Makes a big difference in my experience.