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An ideal massless spring with a spring constant of 2.00 N/m is attached to an object of 75.0 g. The system has a small amount of damping. If the amplitude of the oscillations decreases from 10.0 mm to 5.00 mm in 15.0 s, what is the magnitude of the damping constant b

1 Answer

4 votes

Answer: 0.00693

Step-by-step explanation:

Given

Spring constant
k=2\ N/m

Mass of object
m=75\ g

The amplitude of the oscillation decreases from 10 mm to 5 mm in 15 s

Equation of amplitude for the ideal spring-mass system is


\Rightarrow A=A_oe^{-(bt)/(2m)}\quad \quad [\text{b=damping constant}]\\\text{Insert the values}\\\\\Rightarrow 5=10e^{(b* 15)/(2* 0.075)}\\\\\Rightarrow e^{-(b* 15)/(2* 0.075)}=0.5\\\\\text{Taking natural log both sides}\\\\\Rightarrow \ln \left(e^{-(b* 15)/(2* 0.075)}\right)=\ln 0.5\\\\\Rightarrow -(15b)/(0.15)=-0.693\\\\\Rightarrow b=0.00693

User Chris Forrette
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