The mechanical energy of a damped oscillator becomes half of its initial energy in 4 seconds. In another t seconds its mechanical energy becomes 12.5 % of its initial mechanical energy. Then t=

Step-by-step solution

aligned & at t =4, E = E ₀ 2 & E=E₀ e^ -b t / m E₀ 2 =E₀ e^ - 4 b m & 2= 4 b m & b m = 2 4 & at t , E =12.5 % E ₀ & 12.5 100 E ₀= E ₀ e ^ - bt m 1000 125 = e bt m & (2)^2=e b t m & bt m =2 ^2 & from equation (1), we have & 2 4 t =2 2 & t =8 ~s & aligned