PhysicsThe amplitude of a damped oscillator decreases to 0.9 times its original value in 5s. In another 10s it will decreases to α times its original magnitude, whereα is

The amplitude of a damped oscillator decreases to 0.9 times its original value in 5s. In another 10s it will decreases to α times its original magnitude, whereα is

A
0.81
B
0.9
C
0.729
D
0.656

Solution:

$\begin{array}{l} A = A_{0} \cdot e^{- bt} \\ Case - I : t_{1} = 5 \sec; A = 0 .9 A_{0} \\ 0 .9 A_{0} = A_{0} e^{- b \times 5} \dots \dots \dots (1) \\ Case-II: t_{2} = 5 + 10 = 15 \sec; A = {αA}_{0} \\ {αA}_{0} = A_{0} e^{- b \times 15} \dots \dots \dots (2) \\ α = e^{- b \times 15} = {(e^{- b \times 5})}^{3} = 0 {.9}^{3} = 0 .729 \end{array}$

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