The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5 s. In another 10 s it will decrease to ? times its original magnitude, where equals [2013]

Question

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5 s. In another 10 s it will decrease to $α$ times its original magnitude, where $α$ equals [2013]

Smart Achievers · Accepted Answer

(3)

$∵$ $A = A_{0} e^{- \frac{b t}{2 m}}$

$(where, A_{0} = maximum amplitude)$

According to the question, after $5$ second,

$0.9 A_{0} = A_{0} e^{- \frac{b (5)}{2 m}} ... (i)$

After $10$ more second,

$α A_{0} = A_{0} e^{- \frac{b (15)}{2 m}} ... (ii)$

From $e q^{n} s$ (i) and (ii)

$α = 0.729$

Solution

Q.
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5 s. In another 10 s it will decrease to $α$ times its original magnitude, where $α$ equals [2013]

1 0.7

2 0.81

3 0.729

4 0.6

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