A physicist enters a tall tower and notices a long pendulum that very nearly reaches from the ceiling to the floor. The hanging mass swings back and forth with a period of $12\mathrm{.}0$ s$.$

$($a$)$

Assuming that the pendulum is nearly as long as the tower is tall, what is the tower's height $($in m$)?$

m

$($b$)$

Imagine that the pendulum could be transported to the surface of Mars. If free$-$fall acceleration there is $3\mathrm{.}72$ m$/$s$2,$ with what period $($in seconds$)$ will the pendulum swing?

s