A simple pendulum, has a period of 5.77 seconds. When the pendulum is shortened by 3 m, the period i

For a simple pendulum T = 2π√(L/g), so T² is proportional to L.

Let the old length be L and the new length L − 3. Then 5.77² / 4.60² = L/(L − 3). That is 33.29/21.16 = 1.5733.

1.5733(L − 3) = L, so 0.5733L = 4.72 and L = 8.23 m. New length = 8.23 − 3 = 5.23 m.