Question

a mechanical oscilator has initial energy Enot= 50j having a damping coefficient b=1s. Calculate the time required to decrease to E= Enot/e

Answer 1

Answer

Energy is given

$E=E_0e^{-bt/m}$

Energy is given at time t is $E=\frac{E_0}{e}$

$E_0/e=E_0/e^{t/m} \\ \frac{1}{e}=\frac{1}{e^(t/1)}$

Now calculate

$e=e^{t/1}$

So t=1sec.