An object is hung from a spring, set into vertical vibration, and immersed in a

Question

An object is hung from a spring, set into vertical vibration, and immersed in a beaker of oil. Its motion is graphed in Active Figure 12.14b. The object has mass 375 g, the spring has force constant 100 N/m, and the damping coefficient is b = 0.100 N·s/m.

http://www.webassign.net/serpop/12-14b.gif
Active Figure 12.14b

(a) How long does it take for the amplitude to drop to half its initial value?
______ s

(b) How long does it take for the mechanical energy to drop to half its initial value?
_______s

Explanation / Answer

a)

A(t) = A e^(-bt/2m)

0.5 = e^(-0.1t/(2*0.375))

-0.6931 = -0.1t/(2*0.375)

>>>> t = 5.199 s

b)

E0 = 0.5 k A2

E(t) = 0.5 k (A(t))2

E(t)/E0 = (A(t)/A)2

0.5 = (e^(-0.1t/(2*0.375)))2

0.707107 = e^(-0.1t/(2*0.375))

-0.34657 = -0.1t/(2*0.375)

>>>> t = 2.599 s

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