A simple pendulum has a length of $52\mathrm{.}5$ cm and makes $81\mathrm{.}2$ complete oscillations in $2\mathrm{.}00$ min. The period of the pendulum is $1\mathrm{.}48$ seconds. The value of g at the location of the pendulum is $9\mathrm{.}6$ meters per second.

 $($a$)$ If you increase the length of a pendulum by a factor of exactly $3,$ how does the new period TN compare to the old period T$?$ Express your answer to three significant figures. 

$($b$)$ If you decrease the length of the pendulum by exactly $25\%,$ how does the new period TN compare to the old period T$?$ Express your answer to three significant figures.

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The period T of a simple pendulum is given by the formula T 2 pi sqrtLg where L ... View the full answer