Try this simple test. Bounce the front of the vehicle. When you stop bouncing it, it should stop within 3 bounces. If it doesn't, the shocks are bad. Things like ball joints won't cause it to bounce.
If you find they are bad (and it sounds like they are), here are directions for replacement.
First, here is a link that shows in general how it is done:
Here are the directions specific to your truck for replacement. The pics below correlate with the directions.
2003 Ford Truck F 250 2WD Super Duty V8-5.4L SOHC VIN L
Vehicle Steering and Suspension Suspension Suspension Strut / Shock Absorber Service and Repair Procedures Shock Absorber Front
Shock Absorber-F-250, F-350, Excursion
WARNING: All vehicles are equipped with gas-pressurized shock absorbers which will extend unassisted. Do not apply heat or flame to the shock absorbers during removal or component servicing.
CAUTION: Suspension fasteners are critical parts because they affect performance of vital components and systems and their failure can result in major service expense. They must be replaced with the same part number or an equivalent part if replacement is necessary. Do not use a replacement part of lesser quality or substitute design. Torque values must be used as specified during reassembly to ensure proper retention of these parts.
1. Raise the hood and remove the upper shock absorber retaining nut and upper shock absorber insulator.
2. Raise and support the vehicle.
3. Remove the lower shock absorber retaining nut and remove the shock absorber
1. Using new fasteners, follow the removal procedure in reverse order.
I hope this helps. Let me know if you have other questions.
Take care and God Bless,
Images (Click to enlarge)
Saturday, March 6th, 2021 AT 12:04 AM