The amplitude of a damped harmonic oscillator decreases from $A_0$ to $A_0/2$ in time $t_0$. What wi

Question

The amplitude of a damped harmonic oscillator decreases from $A_0$ to $A_0/2$ in time $t_0$. What will be the amplitude after time $3t_0$?

Professor PC Thomas Classes · Answer

Amplitude in damped SHM decays exponentially: $A(t) = A_0 e^{-\lambda t}$. In time $t_0$, it halves. Therefore, in $3t_0$, it will halve three times: $A_0 	imes (1/2) 	imes (1/2) 	imes (1/2) = A_0/8$.