Physics - EMI/AC Question with Solution | TestHub

For a damped harmonic oscillator, the amplitude $A(t)$ decreases exponentially with time as $A(t)=A_0{e}^{-bt/2m}$, where $b$ is the damping coefficient and $m$ is the mass. Alternatively, we can write $A_n=A_0(1/2{)}^k$ if the amplitude halves every $N$ oscillations, where $k$ is the number of times it has halved.

Given that the amplitude reduces to half ($A_0/2$) in 10 oscillations, we can say that after 10 oscillations, $A_{10}=A_0/2$. This means one 'halving period' corresponds to 10 oscillations. After 30 oscillations, the amplitude will have halved three times (since $30=3\times 10$). So, $A_{30}=A_0\times (1/2)\times (1/2)\times (1/2)=A_0/8$.