Let the original length L=xm

  ;New length =( x -3 ) m

 \(T_1\) = 5.77s; \(T_2\) = 4.60s, 

 \(T^2\) α  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