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The impulse response is correct and you want the function to eventually get to zero. This is representing the wheel oscillation, which will oscillate when excited by a bump and eventually settle.
Side note: from a subjective standpoint, from what I've been told, typically around four oscillations for the settling time said to "feel good," rather than shooting for a critically damped model. A critically damped suspension will be back breaking and the vertical accelerations happen too quickly for a driver to really respond to them.
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