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 [JEE main 2013] ​

Answer 1

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Answer 2

Explanation :- Amplitude of damped oscillator is given by A = A₀e⁻ᵇᵗ/2m

after , 5s , 0.9A₀ = Aₒe⁻ᵇᵗ/2m

⟹ 0.9Aₒ = A₀e⁻ᵇᵗ/2m __________(I)

After , 10s , A = A₀e⁻ᵇᵗ/2m

⟹ A = A₀(e⁻ᵇ¹⁵/2m)

⟹ A = A₀(e⁻⁵ᵇ/2m)³ _______(II)

From eqs (I) and (II ) , We get

A = 0.729A₀

• Hence , α = 0.729 Answer