Question

A 10.6-kg object oscillates at the end of a vertical spring that has a spring constant of 2.05×104

 N/m. The effect of air resistance is represented by the damping coefficient b = 3.00 N ? s/m. (a) Calculate the  frequency of the damped oscillation. (b) By what percentage does the amplitude of the oscillation decrease in each cycle? (c) Find the time interval that elapses while the energy of the system drops to 5.00% of its initial value.

Answer 1

a) $\omega = \sqrt{\omega^2_o-(\frac {b} {2m})^2}$

$=\sqrt {1933.96-0.02}=44.0s^{-1}$

$f=\frac {\omega} {2\pi} =\frac {44.0s^{-1}}{2\pi}$

$f=7.00Hz$

b) $\frac {A_o-A_oe^{-\pi b/m\omega}}{A_o}$

$=0.0.2×100 =2.00\%$

$c) t=10.6s$