P$5\mathrm{.}26$ A pendulum has an oscillation period T which is assumed to depend upon its length L$,$ bob mass m$,$ angle of swing $0,$ and the acceleration of gravity. A pendulum $1$ m long, with a bob mass of $200$ g$,$ is tested on earth and found to have a period of $2\mathrm{.}04$ s when swinging at $20.($a$)$ What is its period when it swings at $45?$ A similarly constructed pendulum, with L $=30$ cm and m $=100$ g$,$ is to swing on the moon $($g $=1\mathrm{.}62$m $/($s $^2))$ at theta $=20$ deg $($b$)$ What will be its period?