What you reflect are two faults, one is the abnormal noise of the engine during cold start, and the other is the cold start jitter. The abnormal starting noise is mostly caused by the problem of matching clearance between starter and flywheel or the damage of one of its components. The engine shakes after the cold car starts. Firstly, consider the influence of carbon deposition, and then check whether the numerical deviation of each sensor is too large, but at present, domestic small-displacement vehicles will have some jitter when they are cold.
I hope the above answers are helpful to you.
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