Question

If you know that the period of a pendulum is 1.87sec. What is the length of that pendulum? (gravity 9.81m/sec squared)

Answer 1

F = m A
m g sin theta = m a = -m d^2 x/dt^2
g sin theta = -d^x/dt^2
for small Theta sin Theta = theta = x/L
g x/L = -d^x/dt^2
let x = c sin 2 pi f t
then v = dx/dt = 2 pif c cos 2 pi f t
and a = d^2x/dt^2 = - (2 pi f)^2 c sin 2 pi f t
so
g /L = (2 pi f)^2
2 pi f = sqrt (g/L)
but T = period = 1/f
so
T = 2 pi sqrt (L/g)
1.87 = 2 pi sqrt(L/9.81)
sqrt(L/9.81) = .2976
L/9.81 = .088577
L = .869 meter