# Critical damping vs Overdamping

## Main Question or Discussion Point

Based on the image provided, why exactly does critical damping allow the system's amplitude to reach 0 more quickly than the case of overdamping? In overdamping, isn't the term in the NEGATIVE exponential greater in absolute value? Wouldn't this cause the system to approach 0 more rapidly? That is, $e^{-( \frac {rt}{2m} + w_d)}$ (overdamping) approaches 0 more rapidly than $e^{- \frac {rt}{2m}}$ (critical damping) since the terms $r, t, m, w_d$ are all positive. Could someone please clarify what's incorrect with my interpretation?

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Orodruin
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