Dampening force - find decrease in amplitude

AI Thread Summary
The discussion revolves around calculating the damping force and its effect on amplitude in a damped harmonic oscillator. The user initially calculates the damping coefficient 'b' as 0.129378 using a specific equation. However, when applying this value to a different mass of 17.7 kg, the resulting amplitude is 50%, which is inconsistent with the expected 59.6%. The user highlights that the amplitude decreases to 45.4% of its initial value, indicating a discrepancy in the calculations. The conversation emphasizes the importance of correctly applying the damping formula to achieve accurate results.
JoeyBob
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Homework Statement
see attached
Relevant Equations
w=sqrt((k/m)-(b/(2m))^2)

Amplitude = (Amax)e^((-b/(2m)t)
So first I tried to find b.

0.454=(0.6)e^((-b/(2*11.6)*50)

Anyways with some natural log algebra etc. I get b = 0.129378

But when I plug this into the same equation only changing mass to 17.7 kg I get 0.4998 or 50% when the answer should be 59.6%?
 

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JoeyBob said:
Amplitude = (Amax)e^((-b/(2m)t)

0.454=(0.6)e^((-b/(2*11.6)*50)
The amplitude decreases to 45.4% of its initial value. So, the final amplitude is not .454
 

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