For a damped oscillator with a mass of 180 g a spring consta

For a damped oscillator with a mass of 180 g, a spring constant 130 N/m and a damping coefficient of 87 g/s, what is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 14 cycles?

Solution

critical damping is
2sqrt(180*130 * 10^-3)=9.6747
=damping ratio=87*10^-3/9.6747=8.99 * 10^-3
v_1/v_1+13=
exp{(2*14*pi*)/sqrt(1-^2)}=
2.204
1/2.204=.45372