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Question:

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

0.81

0.729

0.7

0.6

Solution:

A=A0e⁻ᵏᵗ ⇒0.9A0=A0e⁻⁵ᵏ and αA0=A0e⁻¹⁵ᵏ
solving ⇒α=0.729