The period of a simple pendulum is given by the formula:
T = 2π √(L/g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (9.81 m/s²).
We can use this formula to solve for the length of the new pendulum:
T = 3.683 s
g = 9.81 m/s²
3.683 = 2π √(L/9.81)
Squaring both sides, we get:
(3.683/2π)² = L/9.81
Solving for L, we get:
L = (3.683/2π)² × 9.81
L ≈ 1.561 meters
Therefore, the length of the new pendulum with a period of 3.683 s is approximately 1.561 meters.