Dampening force - find decrease in amplitude

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SUMMARY

The discussion focuses on calculating the damping coefficient 'b' in a damped harmonic oscillator scenario. The user initially calculated 'b' as 0.129378 using the equation 0.454=(0.6)e^((-b/(2*11.6)*50). However, when substituting a mass of 17.7 kg into the same equation, the resulting amplitude was 0.4998, which deviated from the expected 59.6%. The amplitude formula used is Amplitude = (Amax)e^((-b/(2m)t), indicating a misunderstanding in the application of the damping equation.

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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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