A mass of 2.9 g is hanging underneath a spring which has an unknown spring constant. The period of oscillation is 5.5 seconds. Find the spring constant in N/m. Give your answer to 2 s.f.
x = A sin wt
v = A w cos wt
a = -A w^2 sin wt = -w^2 x
F = m a
so
-kx = - m w^2 x
w^2 = k/m
w^2 = k/.0029
w = 18.6 sqrt k
when w t = 2 pi, t = T = 5.5
so
(18.6 sqrt k) (5.5) = 2 pi
sqrt k = .0615
k = .0038