Let the original length L=xm ;New length =( x -3 ) m \(T_1\) = 5.77s; \(T_2\) = 4.60s, \(T^2\) \alpha L ⇒\(T^2\) = kL where K is constant ⇒ K = \(\frac{T^2_1}{L_1} = \frac{T^2_2}{L_2}\) ⇒\(\frac{5.77^2}{x}\) = \(\frac{4.60^2}{x-3}\) ⇒ \(\frac{33.29}{x}\) = \(\frac{4.60^2}{x-3}\) ⇒ 33.29(x-3) = 21.16x ⇒ 33.29x - 99.87 =21.16x ⇒12.13x = 99.87 ;x =\(\frac{99.87}{12.13}\) = 8.23m The new length of the pendulum =x-3 = 8.23-3 =5.23m