Question

a simple pendulum has a period of 4.2 s. when it is shortened by 1.0 m the period is only 3.7 s.
A. without assuming a value for g , calculate the original length of the pendulum

Answer 1

T =2 pi sqrt(L/g) = k sqrt L where k is a constant (on earth)
k sqrt L = 4.2
k sqt (L-1) = 3.7

k^2 L = 17.64
k^2 (L -1) = 13.69

k^2 L / k^2(L-1) = 17.62/13.69
L/(L-1) = 1.287
L = 1.387 L - 1.287
0.387 L = 1.287