Three main problems for Shock Absorber (damper) are below:

First, damper oil becomes solid.
----Actually, damper oil must be with five good characteristics. (1) Good viscosity-temperature characteristics. (2) Lowest flow point to adapt for low temperature. (3) Absolute good characters of resistance to foaming. (4) Good Abrasion resistance、lubrication. (5) Good compatibility with rubber.

Second, abnormal sound.
----it may due to foam in damper oil, it leaks out to lead to friction with damping hole wall.

Three, damper oil leaking.
----to check abnormal leaking.
1. if the nearby parts of seal on outer reservoir surface only occur little oil trace(only Axial direction with about or less than 40 mm very light oil traces), luckly, The damper is on work.
2. If outer reservoir surface occurs much oil (if slowing), then you have to need repair or replace the damper.

Friendly, you can consider those problems above to select a better damper for your car, truck, motorcycle...

Could i let you know more about shock absorber(damper)?

The main parts of it are Piston Rod, Inner tube or named as inner cylinder, Piston, Rebound valve, Outer tube or named as Reservoir tube, Compression valve, Replenishing valve, By-pass valve, Rod Guide or Bearing, Piston and Guide, Dust cover, Oil Seal or Seal.

When you look into the problem of damper, you can take it down and replace some parts if possible.

A Good Suspension must :

1) Provide independent shock absorption to individual wheels. That means, when one wheel rides over a hump, the shock will not be transferred to other wheels.
2) Has adequate body roll. Excessive body roll leads to too much weight transfer thus influence the steering response. It is not comfortable too. Restrict body roll to minimal may create uncomfortable feeling because of excessive g-force. Moreover, body roll could provide information to the driver, telling him the state of cornering and whether the car has reached its limit. Completely eliminate body roll is not at all good.

3) Has a good geometry such that wheel cambers remain unchanged in all conditions, that is, acceleration, braking, cornering, load and bumps.

Body roll suppression usually conflict with ride comfort, because the former requires stiffer spring and dampers while the latter vice versa. Nevertheless, clever suspension geometry may improve body roll without altering the ride.

The most important part for shock absorber:
1、 Tube

2、piston rod

3、Oil Seal

4、Oil

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Are you sure if it's just how the car behaves in its natural state or bad shocks?

Firstly, you can go a simple self-inspection. That is “bounce test”. Parking your car in a flat road, and putting down the front bumper as low as you can, then stand away to check how many bounces your car have… If the bounce up and down is more than twice, then it indicates worn, bad shocks.

Secondly, there will be many sad signs for bad or worn shocks.
1. Is there a noise sounds from suspension?
2. Is there an oil trace on the shocks?
3. Does your car body, suspension lean a bit?
4. To check your tire wear whether the shape resembles “cups” ”scalloping”.
Any one above indicates bad shocks.
Of course, if you feel very dumpy during your driving. It also needs to check your shocks.

Hope it is helpful for you.