Question

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude is $5s$. In another $10s$ it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals.

• A. $0.81$
• B. $0.729$
• C. $0.6$
• D. $0.7$

Answer 1

Answer: (B)

$0.729$

$A=A_0{e}^{-kt}$
$\Rightarrow 0.9A_0=A_0{e}^{-5k}$
and $\alpha A_0=A_0{e}^{-15k}$ solving $\Rightarrow \alpha =0.729$