How could I make a part/model shake realistically based on characters movement

how can I do this?
for example, if a part is welded to the characters back and the character moves, the part will shake realistically following the velocity etc

could a spring be used for this>?

You could definitely use springs and other joints (such as ball-in-sockets) for your movement.
Good examples to look into would be car suspensions, or Soft Body Action shown in some devforum posts, like this one.

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Ive tried looking around on dev fourm but I cant find any examples for this

How could I use a car suspension for this?

Like I said, car suspensions are a good example of how springs are used. You could look into them for an idea on how you can attach your part to the player.

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Ok ill look into this thank you

I cant find a good way to use springs for what i am trying to get

Is there a script that simulates sway on parts based on velocity? maybe like a viewmodel sway