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A 21.2 kg objected oscillates at the end of a vertical spring that has a spring constant $20500 N m^{- 1}$ .The effect of air resistance is represented by the damping coefficient $b = 4 N s m^{- 1}$ .Find the time interval that elapses while the energy of the system drops to 10% of its initial value (Given, $\ln$ 10=2.302)

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$12.2 s$

$24.4 s$

$8.9 s$

answer is B.

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Detailed Solution

$τ = \frac{m}{b} = \frac{21.2}{4} = 5.3 s \Rightarrow E = E_{0} e^{- t / τ} 0.1 = e^{- t / 5.3} \Rightarrow e^{t / 5.3} = 10 \Rightarrow \frac{t}{5.3} = l n 10 t = (5.3) (2.302) = 12.2 s$

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