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

Explanation

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

New length of the pendulum

=x-3 = 8.23-3

=5.23m