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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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