A 0.835-kg block oscillates on the end of a spring whose spring constant is k = 41.0 N/m. The mass moves in a fluid which offers a resistive force F = -bv, where b = 0.662 Ns/m.
a) What is the period of the motion?
b) What is the fractional decrease in amplitude per cycle?
c) Write the displacement as a function of time if at t = 0, x = 0, and t = 1.00 s, x = 0.120m.
m = 0.835 kg
k = 41.0 N/m
b = 0.662 Ns/m
g = -9.80 m/s^2
F = -bv
T (period) = 2*π*√(m/k)
ε = √(k/m) = √(g/l)
l = length
The Attempt at a Solution
a) Since l is not given, I found it, since ε = √(k/m) and ε = √(g/l), therefore √(k/m) = √(g/l)
and l = .1996 m after plugging in the givens and solving for l.
Now, the rest I'm not as sure of:
F = -b*v = -(0.662 Ns/m)(-9.8 m/s^2) ≈ 6.49 N/s
So, using that value in place of g:
T (period) = 2π√(.1996m/6.49N/s) ≈ 1.102 s
^^^ Is that correct? How would I solve for b and c?