Take into account that the period of a pendulum is given by the following expression:
[tex]T=2\pi\sqrt[]{\frac{l}{g}}[/tex]where l is the length of the pendulum and g the acceleration gravitational constant (9.8m/s^2).
In order to determine the new period of the pendulum, first solve the equation above for l, as follow:
[tex]l=\frac{gT^2}{4\pi^2}[/tex]When the priod is T=2.0s, the length l is:
[tex]l=\frac{(9.8\frac{m}{s^2})(2.0s)^2}{4\pi^2}\approx1.0m[/tex]Then, if the length is doubled, that is, if l=2.0m, the new period is:
[tex]T=2\pi\sqrt[]{\frac{2.0m}{9.8\frac{m}{s^2}}}\approx0.45s[/tex]Hence, the new period of the pendulum is approximately 0.45s
