Question

in a damped oscillator m = 250g , k=85N/m, and b = 0.070kg/s. in how many periods of oscillation will the mechanical energy of the oscillator drop to one-half of this initial value?

Answer 1

$$E(t)=E_0e^{-\frac{bt}{m}}=0.5E_0$$

$$t=\frac{m\ln{2}}{b}=\frac{0.25\ln{2}}{0.07}=2.4755\ s$$

The period:

$$T=2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{0.25}{85}}=0.34\ s$$

$$N=\frac{t}{T}=\frac{2.4755}{0.34}=7.3$$