damped oscillation of a mass?

Question

0.050kg mass moves on the end of a spring with k=25 N/m and is acted on by a damping force F=-bv. It is initially displaces at 0.3 m and the amplitude decreases to 0.1 m in 5 sec. What is magnitude of damping constant b?

Answer 1

Natural frequency ω0 = sqrt(k/m)
Period T = 2pi/ω0 = 0.281 s.
We go from measurement of the amplitude ratio to damping constant B via three equations.
Logarithmic decrement (proportional amplitude decrease/cycle) delta = 1/N*ln(A(1)/A(N+1)) (ref. 1), where A = amplitude
A(1)/A(N+1) = 3, ratio reached in 5 s
N = number of cycles = 5/T
delta = 0.06174
zeta = delta/sqrt(4*pi^2+delta^2) (ref. 1)
zeta = 0.009826
B = 2*zeta*ω0*m (ref. 2)
B = 0.02197