A 100 g blob is attached to a vertical spring and the spring stretched 4 cm from its original length.calculate the spring constant, k and period, t

Answer 1

m = .100 Kg
x = .04 meter
F = m g = 9.81(.1) = .981 N
k = F/x = .981/.04 = 24.5 Newtons/meter

let y = A sin 2 pi t/T
F = -ky = -kA sin 2 pi t/T

v = (2 pi /T)A cos 2 pi t/T
a = - (2 pi/T)^2 A sin 2 pi t/T
F = m a
so
k y = m(2 pi /T )^2 y
2 pi/T = sqrt k/m

T = 2 pi sqrt (m/k)
= 2 pi sqrt (.1/24.5)
= 0.401 seconds